Safe Haskell | None |
---|---|

Language | Haskell2010 |

`AUTHOR`

- Dr. Alistair Ward
`DESCRIPTION`

- Exports functions related to
*perfect powers*.

- maybeSquareNumber :: Integral i => i -> Maybe i
- isPerfectPower :: Integral i => i -> Bool

# Functions

maybeSquareNumber :: Integral i => i -> Maybe i Source #

- Returns
`(Just . sqrt)`

if the specified integer is a*square number*(AKA*perfect square*). - https://en.wikipedia.org/wiki/Square_number.
- http://mathworld.wolfram.com/SquareNumber.html.
`(Math.Power.square . sqrt)`

is expensive, so the modulus of the operand is tested first, in an attempt to prove it isn't a*perfect square*. The set of tests, and the valid moduli within each test, are ordered to maximize the rate of failure-detection.

## Predicates

isPerfectPower :: Integral i => i -> Bool Source #

- An integer
`(> 1)`

which can be expressed as an integral power`(> 1)`

of a smaller*natural*number. - CAVEAT:
*zero*and*one*are normally excluded from this set. - https://en.wikipedia.org/wiki/Perfect_power.
- http://mathworld.wolfram.com/PerfectPower.html.
- A generalisation of the concept of
*perfect squares*, in which only the exponent '2' is significant.