Commits

committed b0f7640

• Participants
• Parent commits 3572aa6

File Math/NumberTheory/MoebiusInversion.hs

`   where`
`     triangle n = (n*(n-1)) `quot` 2`
` `
`--- | The generalised Moebius inversion implemented here allows an efficient`
`+-- | @generalInversion g n@ evaluates the generalised Moebius inversion of @g@`
`+--   at the argument @n@.`
`+--`
`+--   The generalised Moebius inversion implemented here allows an efficient`
` --   calculation of isolated values of the function @f : N -> Z@ if the function`
` --   @g@ defined by`
` --`
` --`
` -- >`
` -- > f n = number of reduced proper fractions with denominator <= n`
`+-- >`
` -- > g n = number of proper fractions with denominator <= n`
` -- >`
` --`
` --   Since the function arguments are used as array indices, the domain of`
` --   @f@ is restricted to 'Int'.`
` --`
`---   The value @f n@ is then computed by @generalInversion g n). Note that when`
`+--   The value @f n@ is then computed by @generalInversion g n@). Note that when`
` --   many values of @f@ are needed, there are far more efficient methods, this`
` --   method is only appropriate to compute isolated values of @f@.`
` generalInversion :: (Int -> Integer) -> Int -> Integer`

File Math/NumberTheory/MoebiusInversion/Int.hs

`   where`
`     triangle n = (n*(n-1)) `quot` 2`
` `
`--- | The generalised Moebius inversion implemented here allows an efficient`
`+-- | @generalInversion g n@ evaluates the generalised Moebius inversion of @g@`
`+--   at the argument @n@.`
`+--`
`+--   The generalised Moebius inversion implemented here allows an efficient`
` --   calculation of isolated values of the function @f : N -> Z@ if the function`
` --   @g@ defined by`
` --`
` --   That bears the risk of overflow, however, so be sure to use it only when it's`
` --   safe.`
` --`
`---   The value @f n@ is then computed by @generalInversion g n). Note that when`
`+--   The value @f n@ is then computed by @generalInversion g n@). Note that when`
` --   many values of @f@ are needed, there are far more efficient methods, this`
` --   method is only appropriate to compute isolated values of @f@.`
` generalInversion :: (Int -> Int) -> Int -> Int`