Factory.Math.PerfectPower

AUTHOR

Dr. Alistair Ward

DESCRIPTION

Exports functions related to perfect powers.

Functions

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

• Returns (Just . sqrt) if the specified integer is a square number (AKA perfect square).
• http://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

• 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.
• http://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.