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from __future__ import annotations

def check_polygon(nums: list[float]) -> bool:

"""

Takes list of possible side lengths and determines whether a

two-dimensional polygon with such side lengths can exist.

Returns a boolean value for the < comparison

of the largest side length with sum of the rest.

Wiki: https://en.wikipedia.org/wiki/Triangle_inequality

>>> check_polygon([6, 10, 5])

True

>>> check_polygon([3, 7, 13, 2])

False

>>> check_polygon([1, 4.3, 5.2, 12.2])

False

>>> nums = [3, 7, 13, 2]

>>> _ = check_polygon(nums) # Run function, do not show answer in output

>>> nums # Check numbers are not reordered

[3, 7, 13, 2]

>>> check_polygon([])

Traceback (most recent call last):

...

ValueError: Monogons and Digons are not polygons in the Euclidean space

>>> check_polygon([-2, 5, 6])

Traceback (most recent call last):

...

ValueError: All values must be greater than 0

"""

if len(nums) < 2:

raise ValueError("Monogons and Digons are not polygons in the Euclidean space")

if any(i <= 0 for i in nums):

raise ValueError("All values must be greater than 0")

copy_nums = nums.copy()

copy_nums.sort()

return copy_nums[-1] < sum(copy_nums[:-1])

if __name__ == "__main__":

import doctest

doctest.testmod()

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