Copyright	(c) 2015-2019 Frederick Schneider
License	MIT
Maintainer	Frederick Schneider <fws.nyc@gmail.com>
Stability	Provisional
Safe Haskell	None
Language	Haskell2010

Math.NumberTheory.Canon.Simple

Description

This a wrapper for the Canonical Representation type found in the Internals module. If you want to work with arbitrarily nested prime towers, you can use the Math.NumberTheory.Canon module.

Synopsis

newtype SimpleCanon = MakeSC CR_
type SC = SimpleCanon
toSimpleCanon :: CanonConv a => a -> SimpleCanon
toSC :: CanonConv c => c -> SimpleCanon
toSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> SimpleCanon
fromSimpleCanon :: SimpleCanon -> CR_
fromSC :: SimpleCanon -> CR_
class CanonConv c
scGCD :: SimpleCanon -> SimpleCanon -> SimpleCanon
scLCM :: SimpleCanon -> SimpleCanon -> SimpleCanon
scLog :: SimpleCanon -> Rational
scLogDouble :: SimpleCanon -> Double
scNegative :: SimpleCanon -> Bool
scPositive :: SimpleCanon -> Bool
scToInteger :: SimpleCanon -> Integer
scToI :: SimpleCanon -> Integer
newtype RationalSimpleCanon = MakeRC CR_
type RC = RationalSimpleCanon
toRationalSimpleCanon :: CanonConv a => a -> RationalSimpleCanon
toRC :: CanonConv c => c -> RationalSimpleCanon
toRationalSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> RationalSimpleCanon
fromRationalSimpleCanon :: RationalSimpleCanon -> CR_
fromRC :: RationalSimpleCanon -> CR_
rcNegative :: RationalSimpleCanon -> Bool
rcPositive :: RationalSimpleCanon -> Bool
getNumer :: RationalSimpleCanon -> SimpleCanon
getDenom :: RationalSimpleCanon -> SimpleCanon
getNumerDenom :: RationalSimpleCanon -> (SimpleCanon, SimpleCanon)
getNumerAsRC :: RationalSimpleCanon -> RationalSimpleCanon
getDenomAsRC :: RationalSimpleCanon -> RationalSimpleCanon
getNumerDenomAsRCs :: RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon)
rcLog :: RationalSimpleCanon -> Rational
rcLogDouble :: RationalSimpleCanon -> Double
(>^) :: SimpleCanonRoot a b c => a -> b -> c
(<^) :: SimpleCanonExpnt a b c => a -> b -> c
(%) :: Integral a => a -> a -> a
class SimpleCanonRoot a b c | a b -> c
class SimpleCanonExpnt a b c | a b -> c

Documentation

newtype SimpleCanon Source #

SimpleCanon is a new type wrapping a canonical representation.

Constructors

MakeSC CR_

Instances

Enum SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods succ :: SimpleCanon -> SimpleCanon # pred :: SimpleCanon -> SimpleCanon # toEnum :: Int -> SimpleCanon # fromEnum :: SimpleCanon -> Int # enumFrom :: SimpleCanon -> [SimpleCanon] # enumFromThen :: SimpleCanon -> SimpleCanon -> [SimpleCanon] # enumFromTo :: SimpleCanon -> SimpleCanon -> [SimpleCanon] # enumFromThenTo :: SimpleCanon -> SimpleCanon -> SimpleCanon -> [SimpleCanon] #
Eq SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (==) :: SimpleCanon -> SimpleCanon -> Bool # (/=) :: SimpleCanon -> SimpleCanon -> Bool #
Fractional SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (/) :: SimpleCanon -> SimpleCanon -> SimpleCanon # recip :: SimpleCanon -> SimpleCanon # fromRational :: Rational -> SimpleCanon #
Integral SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods quot :: SimpleCanon -> SimpleCanon -> SimpleCanon # rem :: SimpleCanon -> SimpleCanon -> SimpleCanon # div :: SimpleCanon -> SimpleCanon -> SimpleCanon # mod :: SimpleCanon -> SimpleCanon -> SimpleCanon # quotRem :: SimpleCanon -> SimpleCanon -> (SimpleCanon, SimpleCanon) # divMod :: SimpleCanon -> SimpleCanon -> (SimpleCanon, SimpleCanon) # toInteger :: SimpleCanon -> Integer #
Num SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (+) :: SimpleCanon -> SimpleCanon -> SimpleCanon # (-) :: SimpleCanon -> SimpleCanon -> SimpleCanon # (*) :: SimpleCanon -> SimpleCanon -> SimpleCanon # negate :: SimpleCanon -> SimpleCanon # abs :: SimpleCanon -> SimpleCanon # signum :: SimpleCanon -> SimpleCanon # fromInteger :: Integer -> SimpleCanon #
Ord SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods compare :: SimpleCanon -> SimpleCanon -> Ordering # (<) :: SimpleCanon -> SimpleCanon -> Bool # (<=) :: SimpleCanon -> SimpleCanon -> Bool # (>) :: SimpleCanon -> SimpleCanon -> Bool # (>=) :: SimpleCanon -> SimpleCanon -> Bool # max :: SimpleCanon -> SimpleCanon -> SimpleCanon # min :: SimpleCanon -> SimpleCanon -> SimpleCanon #
Real SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toRational :: SimpleCanon -> Rational #
Show SimpleCanon Source #	Define various instances
Instance details Defined in Math.NumberTheory.Canon.Simple Methods showsPrec :: Int -> SimpleCanon -> ShowS # show :: SimpleCanon -> String # showList :: [SimpleCanon] -> ShowS #
CanonConv SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toSC :: SimpleCanon -> SimpleCanon Source # toRC :: SimpleCanon -> RationalSimpleCanon Source #
SimpleCanonRoot Integer Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> Integer -> SimpleCanon Source #
SimpleCanonRoot Integer SimpleCanon SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> SimpleCanon -> SimpleCanon Source #
SimpleCanonRoot SimpleCanon Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: SimpleCanon -> Integer -> SimpleCanon Source #
SimpleCanonRoot SimpleCanon SimpleCanon SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: SimpleCanon -> SimpleCanon -> SimpleCanon Source #
SimpleCanonExpnt Integer Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: Integer -> Integer -> SimpleCanon Source #
SimpleCanonExpnt RationalSimpleCanon SimpleCanon RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: RationalSimpleCanon -> SimpleCanon -> RationalSimpleCanon Source #
SimpleCanonExpnt SimpleCanon Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: SimpleCanon -> Integer -> SimpleCanon Source #

type SC = SimpleCanon Source #

Shorthand type declaration

toSimpleCanon :: CanonConv a => a -> SimpleCanon Source #

Convert CanonConv types to SimpleCanon.

toSC :: CanonConv c => c -> SimpleCanon Source #

Convert a type to a SimpleCanon.

toSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> SimpleCanon Source #

This function allow you to specify a user function when converting a canon rep to an SC.

fromSimpleCanon :: SimpleCanon -> CR_ Source #

Grab the canon rep from a SimpleCanon.

fromSC :: SimpleCanon -> CR_ Source #

Grab the canon rep from a SimpleCanon.

class CanonConv c Source #

Typeclass for converting to SimpleCanon and RationalSimpleCanon

Minimal complete definition

toSC, toRC

Instances

CanonConv CR_ Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toSC :: CR_ -> SimpleCanon Source # toRC :: CR_ -> RationalSimpleCanon Source #
CanonConv RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toSC :: RationalSimpleCanon -> SimpleCanon Source # toRC :: RationalSimpleCanon -> RationalSimpleCanon Source #
CanonConv SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toSC :: SimpleCanon -> SimpleCanon Source # toRC :: SimpleCanon -> RationalSimpleCanon Source #
CanonConv Canon Source #	Instance of CanonConv class
Instance details Defined in Math.NumberTheory.Canon Methods toSC :: Canon -> SimpleCanon Source # toRC :: Canon -> RationalSimpleCanon Source #

scGCD :: SimpleCanon -> SimpleCanon -> SimpleCanon Source #

SimpleCanon GCD and LCM functions

scLCM :: SimpleCanon -> SimpleCanon -> SimpleCanon Source #

SimpleCanon GCD and LCM functions

scLog :: SimpleCanon -> Rational Source #

Wrapper for underlying CR function

scLogDouble :: SimpleCanon -> Double Source #

Wrapper for underlying CR function

scNegative :: SimpleCanon -> Bool Source #

Wrappers for underlying canon rep functions

scPositive :: SimpleCanon -> Bool Source #

Wrappers for underlying canon rep functions

scToInteger :: SimpleCanon -> Integer Source #

Convert a SimpleCanon back to an Integer.

scToI :: SimpleCanon -> Integer Source #

Convert a SimpleCanon back to an Integer.

newtype RationalSimpleCanon Source #

Newtype for RationalSimpleCanon. The underlying canon rep is the same.

Constructors

MakeRC CR_

Instances

Enum RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods succ :: RationalSimpleCanon -> RationalSimpleCanon # pred :: RationalSimpleCanon -> RationalSimpleCanon # toEnum :: Int -> RationalSimpleCanon # fromEnum :: RationalSimpleCanon -> Int # enumFrom :: RationalSimpleCanon -> [RationalSimpleCanon] # enumFromThen :: RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon] # enumFromTo :: RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon] # enumFromThenTo :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon -> [RationalSimpleCanon] #
Eq RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (==) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool # (/=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool #
Fractional RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (/) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # recip :: RationalSimpleCanon -> RationalSimpleCanon # fromRational :: Rational -> RationalSimpleCanon #
Integral RationalSimpleCanon Source #	Caveat: These functions will error out (in)directly if there are any negative exponents.
Instance details Defined in Math.NumberTheory.Canon.Simple Methods quot :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # rem :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # div :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # mod :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # quotRem :: RationalSimpleCanon -> RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon) # divMod :: RationalSimpleCanon -> RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon) # toInteger :: RationalSimpleCanon -> Integer #
Num RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (+) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # (-) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # (*) :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # negate :: RationalSimpleCanon -> RationalSimpleCanon # abs :: RationalSimpleCanon -> RationalSimpleCanon # signum :: RationalSimpleCanon -> RationalSimpleCanon # fromInteger :: Integer -> RationalSimpleCanon #
Ord RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods compare :: RationalSimpleCanon -> RationalSimpleCanon -> Ordering # (<) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool # (<=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool # (>) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool # (>=) :: RationalSimpleCanon -> RationalSimpleCanon -> Bool # max :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon # min :: RationalSimpleCanon -> RationalSimpleCanon -> RationalSimpleCanon #
Real RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toRational :: RationalSimpleCanon -> Rational #
Show RationalSimpleCanon Source #	Define various instances for RationSimpleCanon.
Instance details Defined in Math.NumberTheory.Canon.Simple Methods showsPrec :: Int -> RationalSimpleCanon -> ShowS # show :: RationalSimpleCanon -> String # showList :: [RationalSimpleCanon] -> ShowS #
CanonConv RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods toSC :: RationalSimpleCanon -> SimpleCanon Source # toRC :: RationalSimpleCanon -> RationalSimpleCanon Source #
SimpleCanonRoot Integer RationalSimpleCanon RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> RationalSimpleCanon -> RationalSimpleCanon Source #
SimpleCanonExpnt RationalSimpleCanon Integer RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: RationalSimpleCanon -> Integer -> RationalSimpleCanon Source #
SimpleCanonExpnt RationalSimpleCanon SimpleCanon RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: RationalSimpleCanon -> SimpleCanon -> RationalSimpleCanon Source #

type RC = RationalSimpleCanon Source #

Shorthand type name

toRationalSimpleCanon :: CanonConv a => a -> RationalSimpleCanon Source #

Convert CanonConv types to RationalSimpleCanon.

toRC :: CanonConv c => c -> RationalSimpleCanon Source #

Convert a type to a RationalSimpleCanon.

toRationalSimpleCanonViaUserFunc :: CR_ -> (Integer -> Bool) -> RationalSimpleCanon Source #

Convert canon rep to RationalSimpleCanon via a user-supplied criterion function.

fromRationalSimpleCanon :: RationalSimpleCanon -> CR_ Source #

Convert RC back to underlying canon rep.

fromRC :: RationalSimpleCanon -> CR_ Source #

Convert RC back to underlying canon rep.

rcNegative :: RationalSimpleCanon -> Bool Source #

Wraps underlying canon rep functions.

rcPositive :: RationalSimpleCanon -> Bool Source #

Wraps underlying canon rep functions.

getNumer :: RationalSimpleCanon -> SimpleCanon Source #

Pulls numerator or denominator from RC and converts it to a SimpleCanon.

getDenom :: RationalSimpleCanon -> SimpleCanon Source #

Pulls numerator or denominator from RC and converts it to a SimpleCanon.

getNumerDenom :: RationalSimpleCanon -> (SimpleCanon, SimpleCanon) Source #

Wraps crSplit function and returns a pair of SimpleCanons.

getNumerAsRC :: RationalSimpleCanon -> RationalSimpleCanon Source #

Calls underlying canon rep function.

getDenomAsRC :: RationalSimpleCanon -> RationalSimpleCanon Source #

Calls underlying canon rep function.

getNumerDenomAsRCs :: RationalSimpleCanon -> (RationalSimpleCanon, RationalSimpleCanon) Source #

Wraps crSplit function and returns a pair of RationalSimpleCanons.

rcLog :: RationalSimpleCanon -> Rational Source #

Calls underlying canon rep function.

rcLogDouble :: RationalSimpleCanon -> Double Source #

Calls underlying canon rep function.

(>^) :: SimpleCanonRoot a b c => a -> b -> c infixr 9 Source #

Root Operator

(<^) :: SimpleCanonExpnt a b c => a -> b -> c infixr 9 Source #

Exponentiation Operator

(%) :: Integral a => a -> a -> a infixl 7 Source #

Modulus operator

class SimpleCanonRoot a b c | a b -> c Source #

Multi-param typeclass for radical/root operator

Minimal complete definition

(>^)

Instances

SimpleCanonRoot Integer Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> Integer -> SimpleCanon Source #
SimpleCanonRoot Integer RationalSimpleCanon RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> RationalSimpleCanon -> RationalSimpleCanon Source #
SimpleCanonRoot Integer SimpleCanon SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: Integer -> SimpleCanon -> SimpleCanon Source #
SimpleCanonRoot SimpleCanon Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: SimpleCanon -> Integer -> SimpleCanon Source #
SimpleCanonRoot SimpleCanon SimpleCanon SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (>^) :: SimpleCanon -> SimpleCanon -> SimpleCanon Source #

class SimpleCanonExpnt a b c | a b -> c Source #

Multi-param typeclass for exponentiation

Minimal complete definition

(<^)

Instances

SimpleCanonExpnt Integer Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: Integer -> Integer -> SimpleCanon Source #
SimpleCanonExpnt RationalSimpleCanon Integer RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: RationalSimpleCanon -> Integer -> RationalSimpleCanon Source #
SimpleCanonExpnt RationalSimpleCanon SimpleCanon RationalSimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: RationalSimpleCanon -> SimpleCanon -> RationalSimpleCanon Source #
SimpleCanonExpnt SimpleCanon Integer SimpleCanon Source #
Instance details Defined in Math.NumberTheory.Canon.Simple Methods (<^) :: SimpleCanon -> Integer -> SimpleCanon Source #