#### Minkowski Distance

p
```def minkowski_distance(
point_a: list[float],
point_b: list[float],
order: int,
) -> float:
"""
This function calculates the Minkowski distance for a given order between
two n-dimensional points represented as lists. For the case of order = 1,
the Minkowski distance degenerates to the Manhattan distance. For
order = 2, the usual Euclidean distance is obtained.

https://en.wikipedia.org/wiki/Minkowski_distance

Note: due to floating point calculation errors the output of this
function may be inaccurate.

>>> minkowski_distance([1.0, 1.0], [2.0, 2.0], 1)
2.0
>>> minkowski_distance([1.0, 2.0, 3.0, 4.0], [5.0, 6.0, 7.0, 8.0], 2)
8.0
>>> import numpy as np
>>> np.isclose(5.0, minkowski_distance([5.0], [0.0], 3))
True
>>> minkowski_distance([1.0], [2.0], -1)
Traceback (most recent call last):
...
ValueError: The order must be greater than or equal to 1.
>>> minkowski_distance([1.0], [1.0, 2.0], 1)
Traceback (most recent call last):
...
ValueError: Both points must have the same dimension.
"""
if order < 1:
raise ValueError("The order must be greater than or equal to 1.")

if len(point_a) != len(point_b):
raise ValueError("Both points must have the same dimension.")

return sum(abs(a - b) ** order for a, b in zip(point_a, point_b)) ** (1 / order)

if __name__ == "__main__":
import doctest

doctest.testmod()
```  