Text.Printer.Fractional

Print fractions.

Positional numeral systems

class PositionalSystem s where

Positional numeral system.

Minimal complete definition

systemName, radixIn, isDigitIn, isNzDigitIn, fromDigitIn, fromNzDigitIn, unsafeFromDigitIn, intToDigitIn

Methods

systemName :: s -> String

The name of the system (e.g. "binary", "decimal").

radixIn :: Num α => s -> α

The radix of the system.

isDigitIn :: s -> Char -> Bool

Test if a character is a digit.

isNzDigitIn :: s -> Char -> Bool

Test if a character is a non-zero digit.

fromDigitIn :: Num α => s -> Char -> Maybe α

Map digits to the corresponding numbers. Return Nothing on other inputs.

fromNzDigitIn :: Num α => s -> Char -> Maybe α

Map non-zero digits to the corresponding numbers. Return Nothing on other inputs.

unsafeFromDigitIn :: Num α => s -> Char -> α

Map digits to the corresponding numbers. No checks are performed.

intToDigitIn :: s -> Int -> Char

Map Int values to the corresponding digits. Inputs must be non-negative and less than the radix.

printDigitIn :: Printer p => s -> Char -> p

Print a digit.

printZeroIn :: Printer p => s -> p

Instances

PositionalSystem UpHex

Defined in Text.Printer.Integral

Methods

systemName :: UpHex -> String

radixIn :: Num α => UpHex -> α

isDigitIn :: UpHex -> Char -> Bool

isNzDigitIn :: UpHex -> Char -> Bool

fromDigitIn :: Num α => UpHex -> Char -> Maybe α

fromNzDigitIn :: Num α => UpHex -> Char -> Maybe α

unsafeFromDigitIn :: Num α => UpHex -> Char -> α

intToDigitIn :: UpHex -> Int -> Char

printDigitIn :: Printer p => UpHex -> Char -> p

printZeroIn :: Printer p => UpHex -> p

PositionalSystem LowHex

Defined in Text.Printer.Integral

Methods

systemName :: LowHex -> String

radixIn :: Num α => LowHex -> α

isDigitIn :: LowHex -> Char -> Bool

isNzDigitIn :: LowHex -> Char -> Bool

fromDigitIn :: Num α => LowHex -> Char -> Maybe α

fromNzDigitIn :: Num α => LowHex -> Char -> Maybe α

unsafeFromDigitIn :: Num α => LowHex -> Char -> α

intToDigitIn :: LowHex -> Int -> Char

printDigitIn :: Printer p => LowHex -> Char -> p

printZeroIn :: Printer p => LowHex -> p

PositionalSystem Hexadecimal

Defined in Text.Printer.Integral

Methods

systemName :: Hexadecimal -> String

radixIn :: Num α => Hexadecimal -> α

isDigitIn :: Hexadecimal -> Char -> Bool

isNzDigitIn :: Hexadecimal -> Char -> Bool

fromDigitIn :: Num α => Hexadecimal -> Char -> Maybe α

fromNzDigitIn :: Num α => Hexadecimal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Hexadecimal -> Char -> α

intToDigitIn :: Hexadecimal -> Int -> Char

printDigitIn :: Printer p => Hexadecimal -> Char -> p

printZeroIn :: Printer p => Hexadecimal -> p

PositionalSystem Decimal

Defined in Text.Printer.Integral

Methods

systemName :: Decimal -> String

radixIn :: Num α => Decimal -> α

isDigitIn :: Decimal -> Char -> Bool

isNzDigitIn :: Decimal -> Char -> Bool

fromDigitIn :: Num α => Decimal -> Char -> Maybe α

fromNzDigitIn :: Num α => Decimal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Decimal -> Char -> α

intToDigitIn :: Decimal -> Int -> Char

printDigitIn :: Printer p => Decimal -> Char -> p

printZeroIn :: Printer p => Decimal -> p

PositionalSystem Octal

Defined in Text.Printer.Integral

Methods

systemName :: Octal -> String

radixIn :: Num α => Octal -> α

isDigitIn :: Octal -> Char -> Bool

isNzDigitIn :: Octal -> Char -> Bool

fromDigitIn :: Num α => Octal -> Char -> Maybe α

fromNzDigitIn :: Num α => Octal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Octal -> Char -> α

intToDigitIn :: Octal -> Int -> Char

printDigitIn :: Printer p => Octal -> Char -> p

printZeroIn :: Printer p => Octal -> p

PositionalSystem Binary

Defined in Text.Printer.Integral

Methods

systemName :: Binary -> String

radixIn :: Num α => Binary -> α

isDigitIn :: Binary -> Char -> Bool

isNzDigitIn :: Binary -> Char -> Bool

fromDigitIn :: Num α => Binary -> Char -> Maybe α

fromNzDigitIn :: Num α => Binary -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Binary -> Char -> α

intToDigitIn :: Binary -> Int -> Char

printDigitIn :: Printer p => Binary -> Char -> p

printZeroIn :: Printer p => Binary -> p

class PositionalSystem s => BitSystem s where

Positonal numeral system with a power of two radix.

Methods

digitBitsIn :: s -> Int

Numer of bits occupied by a digit.

digitMaskIn :: Num α => s -> α

The number that has digitBitsIn least significant bits set to ones and all the other bits set to zeroes.

lastDigitIn :: Bits α => s -> α -> Int

Map the last digit of a number to the corresponding Int value.

Instances

BitSystem UpHex

Defined in Text.Printer.Integral

Methods

digitBitsIn :: UpHex -> Int

digitMaskIn :: Num α => UpHex -> α

lastDigitIn :: Bits α => UpHex -> α -> Int

BitSystem LowHex

Defined in Text.Printer.Integral

Methods

digitBitsIn :: LowHex -> Int

digitMaskIn :: Num α => LowHex -> α

lastDigitIn :: Bits α => LowHex -> α -> Int

BitSystem Hexadecimal

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Hexadecimal -> Int

digitMaskIn :: Num α => Hexadecimal -> α

lastDigitIn :: Bits α => Hexadecimal -> α -> Int

BitSystem Octal

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Octal -> Int

digitMaskIn :: Num α => Octal -> α

lastDigitIn :: Bits α => Octal -> α -> Int

BitSystem Binary

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Binary -> Int

digitMaskIn :: Num α => Binary -> α

lastDigitIn :: Bits α => Binary -> α -> Int

data Binary

The binary numeral system.

Constructors

Binary

Instances

Eq Binary

Defined in Text.Printer.Integral

Methods

(==) :: Binary -> Binary -> Bool

(/=) :: Binary -> Binary -> Bool

Ord Binary

Defined in Text.Printer.Integral

Methods

compare :: Binary -> Binary -> Ordering

(<) :: Binary -> Binary -> Bool

(<=) :: Binary -> Binary -> Bool

(>) :: Binary -> Binary -> Bool

(>=) :: Binary -> Binary -> Bool

max :: Binary -> Binary -> Binary

min :: Binary -> Binary -> Binary

Read Binary

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS Binary

readList :: ReadS [Binary]

readPrec :: ReadPrec Binary

readListPrec :: ReadPrec [Binary]

Show Binary

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> Binary -> ShowS

show :: Binary -> String

showList :: [Binary] -> ShowS

Generic Binary

Defined in Text.Printer.Integral

Associated Types

type Rep Binary :: Type -> Type

Methods

from :: Binary -> Rep Binary x

to :: Rep Binary x -> Binary

BitSystem Binary

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Binary -> Int

digitMaskIn :: Num α => Binary -> α

lastDigitIn :: Bits α => Binary -> α -> Int

PositionalSystem Binary

Defined in Text.Printer.Integral

Methods

systemName :: Binary -> String

radixIn :: Num α => Binary -> α

isDigitIn :: Binary -> Char -> Bool

isNzDigitIn :: Binary -> Char -> Bool

fromDigitIn :: Num α => Binary -> Char -> Maybe α

fromNzDigitIn :: Num α => Binary -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Binary -> Char -> α

intToDigitIn :: Binary -> Int -> Char

printDigitIn :: Printer p => Binary -> Char -> p

printZeroIn :: Printer p => Binary -> p

type Rep Binary

Defined in Text.Printer.Integral

type Rep Binary = D1 (MetaData "Binary" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "Binary" PrefixI False) (U1 :: Type -> Type))

data Octal

The octal numeral system.

Constructors

Octal

Instances

Eq Octal

Defined in Text.Printer.Integral

Methods

(==) :: Octal -> Octal -> Bool

(/=) :: Octal -> Octal -> Bool

Ord Octal

Defined in Text.Printer.Integral

Methods

compare :: Octal -> Octal -> Ordering

(<) :: Octal -> Octal -> Bool

(<=) :: Octal -> Octal -> Bool

(>) :: Octal -> Octal -> Bool

(>=) :: Octal -> Octal -> Bool

max :: Octal -> Octal -> Octal

min :: Octal -> Octal -> Octal

Read Octal

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS Octal

readList :: ReadS [Octal]

readPrec :: ReadPrec Octal

readListPrec :: ReadPrec [Octal]

Show Octal

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> Octal -> ShowS

show :: Octal -> String

showList :: [Octal] -> ShowS

Generic Octal

Defined in Text.Printer.Integral

Associated Types

type Rep Octal :: Type -> Type

Methods

from :: Octal -> Rep Octal x

to :: Rep Octal x -> Octal

BitSystem Octal

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Octal -> Int

digitMaskIn :: Num α => Octal -> α

lastDigitIn :: Bits α => Octal -> α -> Int

PositionalSystem Octal

Defined in Text.Printer.Integral

Methods

systemName :: Octal -> String

radixIn :: Num α => Octal -> α

isDigitIn :: Octal -> Char -> Bool

isNzDigitIn :: Octal -> Char -> Bool

fromDigitIn :: Num α => Octal -> Char -> Maybe α

fromNzDigitIn :: Num α => Octal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Octal -> Char -> α

intToDigitIn :: Octal -> Int -> Char

printDigitIn :: Printer p => Octal -> Char -> p

printZeroIn :: Printer p => Octal -> p

type Rep Octal

Defined in Text.Printer.Integral

type Rep Octal = D1 (MetaData "Octal" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "Octal" PrefixI False) (U1 :: Type -> Type))

data Decimal

The decimal numeral system.

Constructors

Decimal

Instances

Eq Decimal

Defined in Text.Printer.Integral

Methods

(==) :: Decimal -> Decimal -> Bool

(/=) :: Decimal -> Decimal -> Bool

Ord Decimal

Defined in Text.Printer.Integral

Methods

compare :: Decimal -> Decimal -> Ordering

(<) :: Decimal -> Decimal -> Bool

(<=) :: Decimal -> Decimal -> Bool

(>) :: Decimal -> Decimal -> Bool

(>=) :: Decimal -> Decimal -> Bool

max :: Decimal -> Decimal -> Decimal

min :: Decimal -> Decimal -> Decimal

Read Decimal

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS Decimal

readList :: ReadS [Decimal]

readPrec :: ReadPrec Decimal

readListPrec :: ReadPrec [Decimal]

Show Decimal

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> Decimal -> ShowS

show :: Decimal -> String

showList :: [Decimal] -> ShowS

Generic Decimal

Defined in Text.Printer.Integral

Associated Types

type Rep Decimal :: Type -> Type

Methods

from :: Decimal -> Rep Decimal x

to :: Rep Decimal x -> Decimal

PositionalSystem Decimal

Defined in Text.Printer.Integral

Methods

systemName :: Decimal -> String

radixIn :: Num α => Decimal -> α

isDigitIn :: Decimal -> Char -> Bool

isNzDigitIn :: Decimal -> Char -> Bool

fromDigitIn :: Num α => Decimal -> Char -> Maybe α

fromNzDigitIn :: Num α => Decimal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Decimal -> Char -> α

intToDigitIn :: Decimal -> Int -> Char

printDigitIn :: Printer p => Decimal -> Char -> p

printZeroIn :: Printer p => Decimal -> p

type Rep Decimal

Defined in Text.Printer.Integral

type Rep Decimal = D1 (MetaData "Decimal" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "Decimal" PrefixI False) (U1 :: Type -> Type))

data Hexadecimal

The hexadecimal numeral system.

Constructors

Hexadecimal

Instances

Eq Hexadecimal

Defined in Text.Printer.Integral

Methods

(==) :: Hexadecimal -> Hexadecimal -> Bool

(/=) :: Hexadecimal -> Hexadecimal -> Bool

Ord Hexadecimal

Defined in Text.Printer.Integral

Methods

compare :: Hexadecimal -> Hexadecimal -> Ordering

(<) :: Hexadecimal -> Hexadecimal -> Bool

(<=) :: Hexadecimal -> Hexadecimal -> Bool

(>) :: Hexadecimal -> Hexadecimal -> Bool

(>=) :: Hexadecimal -> Hexadecimal -> Bool

max :: Hexadecimal -> Hexadecimal -> Hexadecimal

min :: Hexadecimal -> Hexadecimal -> Hexadecimal

Read Hexadecimal

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS Hexadecimal

readList :: ReadS [Hexadecimal]

readPrec :: ReadPrec Hexadecimal

readListPrec :: ReadPrec [Hexadecimal]

Show Hexadecimal

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> Hexadecimal -> ShowS

show :: Hexadecimal -> String

showList :: [Hexadecimal] -> ShowS

Generic Hexadecimal

Defined in Text.Printer.Integral

Associated Types

type Rep Hexadecimal :: Type -> Type

Methods

from :: Hexadecimal -> Rep Hexadecimal x

to :: Rep Hexadecimal x -> Hexadecimal

BitSystem Hexadecimal

Defined in Text.Printer.Integral

Methods

digitBitsIn :: Hexadecimal -> Int

digitMaskIn :: Num α => Hexadecimal -> α

lastDigitIn :: Bits α => Hexadecimal -> α -> Int

PositionalSystem Hexadecimal

Defined in Text.Printer.Integral

Methods

systemName :: Hexadecimal -> String

radixIn :: Num α => Hexadecimal -> α

isDigitIn :: Hexadecimal -> Char -> Bool

isNzDigitIn :: Hexadecimal -> Char -> Bool

fromDigitIn :: Num α => Hexadecimal -> Char -> Maybe α

fromNzDigitIn :: Num α => Hexadecimal -> Char -> Maybe α

unsafeFromDigitIn :: Num α => Hexadecimal -> Char -> α

intToDigitIn :: Hexadecimal -> Int -> Char

printDigitIn :: Printer p => Hexadecimal -> Char -> p

printZeroIn :: Printer p => Hexadecimal -> p

type Rep Hexadecimal

Defined in Text.Printer.Integral

type Rep Hexadecimal = D1 (MetaData "Hexadecimal" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "Hexadecimal" PrefixI False) (U1 :: Type -> Type))

data LowHex

The hexadecimal numeral system, using lower case digits.

Constructors

LowHex

Instances

Eq LowHex

Defined in Text.Printer.Integral

Methods

(==) :: LowHex -> LowHex -> Bool

(/=) :: LowHex -> LowHex -> Bool

Ord LowHex

Defined in Text.Printer.Integral

Methods

compare :: LowHex -> LowHex -> Ordering

(<) :: LowHex -> LowHex -> Bool

(<=) :: LowHex -> LowHex -> Bool

(>) :: LowHex -> LowHex -> Bool

(>=) :: LowHex -> LowHex -> Bool

max :: LowHex -> LowHex -> LowHex

min :: LowHex -> LowHex -> LowHex

Read LowHex

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS LowHex

readList :: ReadS [LowHex]

readPrec :: ReadPrec LowHex

readListPrec :: ReadPrec [LowHex]

Show LowHex

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> LowHex -> ShowS

show :: LowHex -> String

showList :: [LowHex] -> ShowS

Generic LowHex

Defined in Text.Printer.Integral

Associated Types

type Rep LowHex :: Type -> Type

Methods

from :: LowHex -> Rep LowHex x

to :: Rep LowHex x -> LowHex

BitSystem LowHex

Defined in Text.Printer.Integral

Methods

digitBitsIn :: LowHex -> Int

digitMaskIn :: Num α => LowHex -> α

lastDigitIn :: Bits α => LowHex -> α -> Int

PositionalSystem LowHex

Defined in Text.Printer.Integral

Methods

systemName :: LowHex -> String

radixIn :: Num α => LowHex -> α

isDigitIn :: LowHex -> Char -> Bool

isNzDigitIn :: LowHex -> Char -> Bool

fromDigitIn :: Num α => LowHex -> Char -> Maybe α

fromNzDigitIn :: Num α => LowHex -> Char -> Maybe α

unsafeFromDigitIn :: Num α => LowHex -> Char -> α

intToDigitIn :: LowHex -> Int -> Char

printDigitIn :: Printer p => LowHex -> Char -> p

printZeroIn :: Printer p => LowHex -> p

type Rep LowHex

Defined in Text.Printer.Integral

type Rep LowHex = D1 (MetaData "LowHex" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "LowHex" PrefixI False) (U1 :: Type -> Type))

data UpHex

The hexadecimal numeral system, using upper case digits.

Constructors

UpHex

Instances

Eq UpHex

Defined in Text.Printer.Integral

Methods

(==) :: UpHex -> UpHex -> Bool

(/=) :: UpHex -> UpHex -> Bool

Ord UpHex

Defined in Text.Printer.Integral

Methods

compare :: UpHex -> UpHex -> Ordering

(<) :: UpHex -> UpHex -> Bool

(<=) :: UpHex -> UpHex -> Bool

(>) :: UpHex -> UpHex -> Bool

(>=) :: UpHex -> UpHex -> Bool

max :: UpHex -> UpHex -> UpHex

min :: UpHex -> UpHex -> UpHex

Read UpHex

Defined in Text.Printer.Integral

Methods

readsPrec :: Int -> ReadS UpHex

readList :: ReadS [UpHex]

readPrec :: ReadPrec UpHex

readListPrec :: ReadPrec [UpHex]

Show UpHex

Defined in Text.Printer.Integral

Methods

showsPrec :: Int -> UpHex -> ShowS

show :: UpHex -> String

showList :: [UpHex] -> ShowS

Generic UpHex

Defined in Text.Printer.Integral

Associated Types

type Rep UpHex :: Type -> Type

Methods

from :: UpHex -> Rep UpHex x

to :: Rep UpHex x -> UpHex

BitSystem UpHex

Defined in Text.Printer.Integral

Methods

digitBitsIn :: UpHex -> Int

digitMaskIn :: Num α => UpHex -> α

lastDigitIn :: Bits α => UpHex -> α -> Int

PositionalSystem UpHex

Defined in Text.Printer.Integral

Methods

systemName :: UpHex -> String

radixIn :: Num α => UpHex -> α

isDigitIn :: UpHex -> Char -> Bool

isNzDigitIn :: UpHex -> Char -> Bool

fromDigitIn :: Num α => UpHex -> Char -> Maybe α

fromNzDigitIn :: Num α => UpHex -> Char -> Maybe α

unsafeFromDigitIn :: Num α => UpHex -> Char -> α

intToDigitIn :: UpHex -> Int -> Char

printDigitIn :: Printer p => UpHex -> Char -> p

printZeroIn :: Printer p => UpHex -> p

type Rep UpHex

Defined in Text.Printer.Integral

type Rep UpHex = D1 (MetaData "UpHex" "Text.Printer.Integral" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "UpHex" PrefixI False) (U1 :: Type -> Type))

Optionality characteristic

data Optional

Optionality characteristic.

Constructors

Optional

Required

Instances

Bounded Optional

Defined in Text.Printer.Fractional

Methods

minBound :: Optional

maxBound :: Optional

Enum Optional

Defined in Text.Printer.Fractional

Methods

succ :: Optional -> Optional

pred :: Optional -> Optional

toEnum :: Int -> Optional

fromEnum :: Optional -> Int

enumFrom :: Optional -> [Optional]

enumFromThen :: Optional -> Optional -> [Optional]

enumFromTo :: Optional -> Optional -> [Optional]

enumFromThenTo :: Optional -> Optional -> Optional -> [Optional]

Eq Optional

Defined in Text.Printer.Fractional

Methods

(==) :: Optional -> Optional -> Bool

(/=) :: Optional -> Optional -> Bool

Ord Optional

Defined in Text.Printer.Fractional

Methods

compare :: Optional -> Optional -> Ordering

(<) :: Optional -> Optional -> Bool

(<=) :: Optional -> Optional -> Bool

(>) :: Optional -> Optional -> Bool

(>=) :: Optional -> Optional -> Bool

max :: Optional -> Optional -> Optional

min :: Optional -> Optional -> Optional

Read Optional

Defined in Text.Printer.Fractional

Methods

readsPrec :: Int -> ReadS Optional

readList :: ReadS [Optional]

readPrec :: ReadPrec Optional

readListPrec :: ReadPrec [Optional]

Show Optional

Defined in Text.Printer.Fractional

Methods

showsPrec :: Int -> Optional -> ShowS

show :: Optional -> String

showList :: [Optional] -> ShowS

Ix Optional

Defined in Text.Printer.Fractional

Methods

range :: (Optional, Optional) -> [Optional]

index :: (Optional, Optional) -> Optional -> Int

unsafeIndex :: (Optional, Optional) -> Optional -> Int

inRange :: (Optional, Optional) -> Optional -> Bool

rangeSize :: (Optional, Optional) -> Int

unsafeRangeSize :: (Optional, Optional) -> Int

Generic Optional

Defined in Text.Printer.Fractional

Associated Types

type Rep Optional :: Type -> Type

Methods

from :: Optional -> Rep Optional x

to :: Rep Optional x -> Optional

type Rep Optional

Defined in Text.Printer.Fractional

type Rep Optional = D1 (MetaData "Optional" "Text.Printer.Fractional" "text-printer-0.5.0.1-CSY6rOSK9ucLFR29CVeqaN" False) (C1 (MetaCons "Optional" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons "Required" PrefixI False) (U1 :: Type -> Type))

isOptional :: Optional -> Bool

True if the supplied value is Optional and false otherwise.

isRequired :: Optional -> Bool

True if the supplied value is Required and false otherwise.

Fraction printers

fraction'

Arguments

:: (PositionalSystem s, Real α, Printer p)

=> s

-> p

Prefix for negative values

-> p

Zero printer

-> p

Prefix for positive values

-> p

Numerator/denominator separator

-> Optional

Whether to print invisible denominators

-> α

-> p

Print a fraction, writing the numerator and the denominator in the specified positional numeral system.

fraction :: (Real α, Printer p) => α -> p

Print a fraction. The numerator and the denominator are written in the decimal numeral system and separated by a slash. Negative values are prefixed with a minus sign. Invisible denominators are omitted.