Copyright	Anders Claesson 2015
Maintainer	Anders Claesson <anders.claesson@gmail.com>
Safe Haskell	None
Language	Haskell98

HOPS.GF.Rat

Description

License : BSD-3

Rational numbers extended with two elements representing a finite but indeterminate value and divison by zero, respectively.

Synopsis

Documentation

data Rat Source #

Rationals extended with two elements:

Constructors

Val !Rational	A known rational value.
Indet	An unknown value.
DZ	Division by zero.

Instances

Eq Rat Source #
Methods (==) :: Rat -> Rat -> Bool # (/=) :: Rat -> Rat -> Bool #
Floating Rat Source #
Methods pi :: Rat # exp :: Rat -> Rat # log :: Rat -> Rat # sqrt :: Rat -> Rat # (**) :: Rat -> Rat -> Rat # logBase :: Rat -> Rat -> Rat # sin :: Rat -> Rat # cos :: Rat -> Rat # tan :: Rat -> Rat # asin :: Rat -> Rat # acos :: Rat -> Rat # atan :: Rat -> Rat # sinh :: Rat -> Rat # cosh :: Rat -> Rat # tanh :: Rat -> Rat # asinh :: Rat -> Rat # acosh :: Rat -> Rat # atanh :: Rat -> Rat # log1p :: Rat -> Rat # expm1 :: Rat -> Rat # log1pexp :: Rat -> Rat # log1mexp :: Rat -> Rat #
Fractional Rat Source #	Division table: / \| Val 0 \| Val b \| Indet \| DZ ------+-------+-----------+-------+---- Val 0 \| DZ \| Val 0 \| Val 0 \| DZ Val a \| DZ \| Val (a/b) \| Indet \| DZ Indet \| DZ \| Indet \| Indet \| DZ DZ \| DZ \| DZ \| DZ \| DZ
Methods (/) :: Rat -> Rat -> Rat # recip :: Rat -> Rat # fromRational :: Rational -> Rat #
Num Rat Source #	Addition and multiplication tables: + \| Val b \| Indet \| DZ ------+-----------+-------+---- Val a \| Val (a+b) \| Indet \| DZ Indet \| Indet \| Indet \| DZ DZ \| DZ \| DZ \| DZ * \| Val 0 \| Val b \| Indet \| DZ ------+-------+-----------+-------+---- Val 0 \| Val 0 \| Val 0 \| Val 0 \| DZ Val a \| Val 0 \| Val (a*b) \| Indet \| DZ Indet \| Val 0 \| Indet \| Indet \| DZ DZ \| DZ \| DZ \| DZ \| DZ
Methods (+) :: Rat -> Rat -> Rat # (-) :: Rat -> Rat -> Rat # (*) :: Rat -> Rat -> Rat # negate :: Rat -> Rat # abs :: Rat -> Rat # signum :: Rat -> Rat # fromInteger :: Integer -> Rat #
Ord Rat Source #
Methods compare :: Rat -> Rat -> Ordering # (<) :: Rat -> Rat -> Bool # (<=) :: Rat -> Rat -> Bool # (>) :: Rat -> Rat -> Bool # (>=) :: Rat -> Rat -> Bool # max :: Rat -> Rat -> Rat # min :: Rat -> Rat -> Rat #
Read Rat Source #
Methods readsPrec :: Int -> ReadS Rat # readList :: ReadS [Rat] # readPrec :: ReadPrec Rat # readListPrec :: ReadPrec [Rat] #
Show Rat Source #
Methods showsPrec :: Int -> Rat -> ShowS # show :: Rat -> String # showList :: [Rat] -> ShowS #
Pretty Rat Source #
Methods pretty :: Rat -> ByteString Source #

maybeRational :: Rat -> Maybe Rational Source #

maybeRational of Val x is Just x, otherwise it is Nothing.

maybeInteger :: Rat -> Maybe Integer Source #

maybeInteger of Val x is Just the numerator of x if the denominator of x is 1, otherwise it is Nothing.

maybeInt :: Rat -> Maybe Int Source #

Like maybeInteger but return Nothing when the integer is out of range for an Int.

isRational :: Rat -> Bool Source #

Is the given element a rational?

isInteger :: Rat -> Bool Source #

Is the given element an Integer?

isInt :: Rat -> Bool Source #

Is the given element an Int?

factorial :: Rat -> Rat Source #

If the given value represents a nonnegative integer, then the factorial of that integer is returned. If given DZ, return DZ. In all other cases return Indet.

binomial :: Int -> Int -> Integer Source #

choose :: (Integral a, Num b) => a -> a -> b Source #

multinomial :: (Integral b, Fractional a) => [b] -> a Source #