factory-0.3.0.0: Rational arithmetic in an irrational world.

Safe HaskellNone
LanguageHaskell2010

Factory.Math.Implementations.Factorial

Contents

Description

AUTHOR
Dr. Alistair Ward
DESCRIPTION

Synopsis

Types

Data-types

data Algorithm Source #

The algorithms by which factorial has been implemented.

Constructors

Bisection

The integers from which the factorial is composed, are multiplied using Data.Interval.product'.

PrimeFactorisation

The prime factors of the factorial are extracted, then raised to the appropriate power, before multiplication.

Functions

primeFactors Source #

Arguments

:: Integral base 
=> base

The number, whose factorial is to be factorised.

-> Factors base base

The base and exponent of each prime factor in the factorial, ordered by increasing base (and decreasing exponent).

  • Returns the prime factors, of the factorial of the specifed integer.
  • Precisely all the primes less than or equal to the specified integer n, are included in n!; only the multiplicity of each of these known prime components need be determined.
  • https://en.wikipedia.org/wiki/Factorial#Number_theory.
  • CAVEAT: currently a hotspot.

risingFactorial Source #

Arguments

:: (Integral i, Show i) 
=> i

The lower bound of the integer-range, whose product is returned.

-> i

The number of integers in the range above.

-> i

The result.

fallingFactorial Source #

Arguments

:: (Integral i, Show i) 
=> i

The upper bound of the integer-range, whose product is returned.

-> i

The number of integers in the range beneath.

-> i

The result.

Operators

(!/!) infixl 7 Source #

Arguments

:: (Integral i, Fractional f, Show i) 
=> i

The numerator.

-> i

The denominator.

-> f

The resulting fraction.

  • Returns the ratio of two factorials.
  • It is more efficient than evaluating both factorials, and then dividing.
  • For more complex combinations of factorials, such as in the Binomial coefficient, extract the prime factors using primeFactors then manipulate them using the module Data.PrimeFactors, and evaluate it using by Data.PrimeFactors.product'.