| Copyright | (c) 2011 Daniel Fischer |
|---|---|
| License | MIT |
| Maintainer | Daniel Fischer <daniel.is.fischer@googlemail.com> |
| Safe Haskell | None |
| Language | Haskell2010 |
Math.NumberTheory.Powers.Cubes
Description
Functions dealing with cubes. Moderately efficient calculation of integer cube roots and testing for cubeness.
Synopsis
- integerCubeRoot :: Integral a => a -> a
- integerCubeRoot' :: Integral a => a -> a
- exactCubeRoot :: Integral a => a -> Maybe a
- isCube :: Integral a => a -> Bool
- isCube' :: Integral a => a -> Bool
- isPossibleCube :: Integral a => a -> Bool
Documentation
integerCubeRoot :: Integral a => a -> a Source #
Calculate the integer cube root of an integer n,
that is the largest integer r such that r^3 <= n.
Note that this is not symmetric about 0, for example
integerCubeRoot (-2) = (-2) while integerCubeRoot 2 = 1.
integerCubeRoot' :: Integral a => a -> a Source #
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 Source #
Returns Nothing if the argument is not a cube,
Just r if n == r^3.
isCube' :: Integral a => a -> Bool Source #
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 Source #
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.