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| Synopsis |
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| Documentation |
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| powerset :: [a] -> [[a]] |
| Answer all subsets of a set.
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| everywhere :: a -> [a] -> [[a]] |
| Answer a list of lists with the first arg interspersed at all
positions in the list arg.
E.g., everywhere 1 [4,5] yields [[1,4,5],[4,1,5],[4,5,1]].
Copied from http://www.haskell.org/hawiki/LicensedPreludeExts.
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| permutations :: [a] -> [[a]] |
| Answer all permutations of the given list.
Copied from http://www.haskell.org/hawiki/LicensedPreludeExts.
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| permutations_count :: Integral a => a -> a -> a |
| Answer the number of k-permutations from a collection of n objects.
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| combinations :: [a] -> [[a]] |
| Answer a list of all combinations (of any length) of the given list.
Copied from http://www.haskell.org/hawiki/LicensedPreludeExts.
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| combinations_count :: Integral a => a -> a -> a |
| Answer the number of ways to choose k unordered objects from a collection
of n objects.
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| binomial :: Integral a => a -> a -> Ratio a -> Ratio a |
| Answer the probability of an event with probability p occurring r times
in n trials.
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| printBinomial :: Integral a => a -> a -> Ratio a -> IO () |
| Calculate the binomial value with binomial and print the result
as a double with 2 decimal places.
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| binomialSimple :: Integral a => a -> a -> Ratio a |
| Calculate the binomial value assuming that the probability of the event
occurring is 1/n.
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| printBinomialSimple :: Integral a => a -> a -> IO () |
| Calculate the binomial value with binomialSimple and print the
result as a Double with 2 decimal places.
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| ratioToFloating :: (Integral a, Floating b) => Ratio a -> b |
| Answer the given rational as a floating approximation.
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| fareylen :: Integral a => a -> a |
| Calculate the length of the farey sequence with denominator n, including
the value for 0/n and n/n (so subtract 2 if you want the more standard
value excluding these).
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| fareylenf :: Integral a => a -> a |
| Calculate the length of the farey sequence with denominator n, including
the value for 0/n and n/n (so subtract 2 if you want the more standard
value excluding these). This version is optimized for n small enough that
totient n fits in an Int.
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| totient :: Integral a => a -> a |
| Euler's totient function, which calculates the number of positive
integers <=n that are relatively prime to (i.e., do not contain any factor
in common with) n, where 1 is counted as being relatively prime to all
numbers. In number theory, the totient phi(n) of a positive integer n
is defined to be the number of positive integers less than or equal to n and
coprime to n.
http://en.wikipedia.org/wiki/Totient
http://mathworld.wolfram.com/TotientFunction.html
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| polyx :: Integral a => a -> [a] |
| Creates an infinite list of n-gon numbers; e.g., for n = 3, returns
the triangular numbers (1, 3, 6, 10..), and for n = 5, returns the pentagon
numbers (1, 5, 12, 22..).
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| integralToBinary :: Integral a => a -> String |
| Convert an integral number to its binary equivalent as a string.
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| factorial :: Integral a => a -> a |
| Calculate the factorial of a positive integer.
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| factorials :: Array Int Int |
| Array of factorial results of the 10 digits, from 0 to 9.
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| tri :: Integral a => a -> a |
| Calculate the nth triangle number (1, 3, 6, 10..).
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| tris :: Integral a => [a] |
| A stream of triangle numbers.
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| pents :: Integral a => [a] |
| A stream of pentagon numbers.
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| fibs :: Integral a => [a] |
| An infinite list of fibonnaci numbers
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| primes :: Integral a => [a] |
| An infinite list of prime numbers, using a simple implementation of the
sieve of Eratosthenes.
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| primesn :: Integral a => a -> [a] |
| A finite list of prime numbers from 2 to n (inclusive), using a simple
implementation of the sieve of Eratosthenes.
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| divides :: Integral a => a -> a -> Bool |
| Determine if d divides into n evenly.
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| ld :: Integral a => a -> a |
| Determine the least natural number greater than 1 that divides n.
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| ldf :: Integral a => a -> a -> a |
| Determine the least natural number greater than or equal to k that that divides n.
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| isprime :: Integral a => a -> Bool |
| Determine if the given integral argument is a prime number.
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| factors :: Integral a => a -> [a] |
| Determine the unique prime factorization of a positive integer.
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| ufactors :: Integral a => a -> [a] |
| Determine the unique prime factors of a positive integer.
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| divisors :: Integral a => a -> [a] |
| Calculate the proper divisors of n (divides n evenly and less than n).
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| numdivisors :: Integral a => a -> Int |
| Calculate the number of divisors of n, including 1 and n itself.
This implementation relies on the fact that the number of divisors for a
number whose prime factorization is (p1^a) (p2^b) (p3^c)... (px^n) is equal
to (a+1) (b+1) (c+1) ... (n+1).
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| sumdivisors :: Integral a => a -> a |
| Calculate the sum of the divisors of a number.
For example: (72) = 1513 = 195.
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| pnumdivisors :: Integral a => a -> a -> a |
| Calculate the number of divisors of the given prime number raised to the given
power, using the formula (p^(x+1)-1)/(p-1).
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| coprime :: Integral a => a -> a -> Bool |
| Determine if 2 integrals are coprime (have gcd of 1).
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| mean :: Fractional a => [a] -> a |
| Determine the arithmetic mean of a list of one or more numbers.
If the list is empty, 0 is returned.
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| sum_of_n_primes_app :: Integral a => a -> Float |
| Approximate the sum of the first n primes, using the formula (Bach and
Shallit, 1996): sigma n ~ 1/2 * n^2 * ln n
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| sum_of_n_primes :: Integral a => a -> Float |
| Determine the sum of the first n primes. This is very slow. Consider the
function that approximates the sum, sum_of_n_primes_app.
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| modexp :: Integer -> Integer -> Integer -> Integer |
| Calculates x^y modulo N. This algorithm has complexity O(n^3) where
n is the size in bits of the largest of x, y, and N.
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| e_calc :: Int -> Double |
| A formula for computing e, from Courant/Fritz;
it converges quite fast, and already is perfectly
accurate to limits of Double at e_18.
e = 1/0! + 1/1! + 1/2! + ... + 1/n!
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| e_calc' :: Int -> Double |
| Another series for computing e from Courant/Fritz,
but this one is very slow to converge: at e_1000
it is still only 2.7169.
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| Produced by Haddock version 2.4.1 |
