# Compute the volume of an ⟦n⟧-dimensional simplex, given as a list
# of ⟦n + 1⟧ points. A 2D simplex is a triangle, given by 3 points,
# a 3D simplex is a 3-sided pyramid given by 4 points and so on.

def volume( pts ):
    pass

def test_main() -> None:
    from math import isclose
    assert isclose( volume( [ [ 0, 0 ], [ 0, 3 ], [ 4, 0 ] ] ), 6 )
    assert isclose( volume( [ [ 0, 0 ], [ 4, 0 ], [ 3, 0 ] ] ), 0 )
    assert isclose( volume( [ [ 3, 3, 2 ], [ 0, 7, -1 ], [ 3, 1, 4 ], [ 0, -2, 3 ]  ] ), 5 )

if __name__ == "__main__":
    test_main()