| Copyright | (c) 2011 Daniel Fischer |
|---|---|
| License | MIT |
| Maintainer | Daniel Fischer <daniel.is.fischer@googlemail.com> |
| Safe Haskell | None |
| Language | Haskell2010 |
Math.NumberTheory.Powers.Fourth
Description
Functions dealing with fourth powers. Efficient calculation of integer fourth roots and efficient testing for being a square's square.
Synopsis
- integerFourthRoot :: Integral a => a -> a
- integerFourthRoot' :: Integral a => a -> a
- exactFourthRoot :: Integral a => a -> Maybe a
- isFourthPower :: Integral a => a -> Bool
- isFourthPower' :: Integral a => a -> Bool
- isPossibleFourthPower :: Integral a => a -> Bool
Documentation
integerFourthRoot :: Integral a => a -> a Source #
Calculate the integer fourth root of a nonnegative number,
that is, the largest integer r with r^4 <= n.
Throws an error on negaitve input.
integerFourthRoot' :: Integral a => a -> a Source #
Calculate the integer fourth root of a nonnegative number,
that is, the largest integer r with r^4 <= n.
The condition is not checked.
exactFourthRoot :: Integral a => a -> Maybe a Source #
Returns Nothing if n is not a fourth power,
Just r if n == r^4 and r >= 0.
isFourthPower :: Integral a => a -> Bool Source #
Test whether an integer is a fourth power. First nonnegativity is checked, then the unchecked test is called.
isFourthPower' :: Integral a => a -> Bool Source #
Test whether a nonnegative number is a fourth power.
The condition is not checked. If a number passes the
isPossibleFourthPower test, its integer fourth root
is calculated.
isPossibleFourthPower :: Integral a => a -> Bool Source #
Test whether a nonnegative number is a possible fourth power. The condition is not checked. This eliminates about 99.958% of numbers.