Math.NumberTheory.Powers.Cubes

Deprecated: Use Math.NumberTheory.Roots

Description: Deprecated

Functions dealing with cubes. Moderately efficient calculation of integer cube roots and testing for cubeness.

Documentation

integerCubeRoot :: Integral a => a -> a

For a given \( n \) calculate its integer cube root \( \lfloor \sqrt[3]{n} \rfloor \). Note that this is not symmetric about 0.

>>> map integerCubeRoot [7, 8, 9]
[1,2,2]
>>> map integerCubeRoot [-7, -8, -9]
[-2,-2,-3]

integerCubeRoot' :: Integral a => a -> a

Calculate the integer cube root of a nonnegative integer n, that is, the largest integer r such that r^3 <= n. The precondition n >= 0 is not checked.

exactCubeRoot :: Integral a => a -> Maybe a

Calculate the exact integer cube root if it exists, otherwise return Nothing.

>>> map exactCubeRoot [-9, -8, -7, 7, 8, 9]
[Nothing,Just (-2),Nothing,Nothing,Just 2,Nothing]

isCube :: Integral a => a -> Bool

Test whether the argument is a perfect cube.

>>> map isCube [-9, -8, -7, 7, 8, 9]
[False,True,False,False,True,False]

isCube' :: Integral a => a -> Bool

Test whether a nonnegative integer is a cube. Before integerCubeRoot is calculated, a few tests of remainders modulo small primes weed out most non-cubes. For testing many numbers, most of which aren't cubes, this is much faster than let r = cubeRoot n in r*r*r == n. The condition n >= 0 is not checked.

isPossibleCube :: Integral a => a -> Bool

Test whether a nonnegative number is possibly a cube. Only about 0.08% of all numbers pass this test. The precondition n >= 0 is not checked.