-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Statically checked physical dimensions.
--   
--   Dimensional is a library providing data types for performing
--   arithmetic with physical quantities and units. Information about the
--   physical dimensions of the quantities and units is embedded in their
--   types and the validity of operations is verified by the type checker
--   at compile time. The boxing and unboxing of numerical values as
--   quantities is done by multiplication and division with units. The
--   library is designed to, as far as is practical, enforce/encourage best
--   practices of unit usage.
@package dimensional
@version 0.9


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional
newtype Dimensional v d a
Dimensional :: a -> Dimensional v d a
data DUnit
data DQuantity
type Unit = Dimensional DUnit
type Quantity = Dimensional DQuantity
(*~) :: Num a => a -> Unit d a -> Quantity d a
(/~) :: Fractional a => Quantity d a -> Unit d a -> a
data Dim l m t i th n j
type DOne = Dim Zero Zero Zero Zero Zero Zero Zero
type DLength = Dim Pos1 Zero Zero Zero Zero Zero Zero
type DMass = Dim Zero Pos1 Zero Zero Zero Zero Zero
type DTime = Dim Zero Zero Pos1 Zero Zero Zero Zero
type DElectricCurrent = Dim Zero Zero Zero Pos1 Zero Zero Zero
type DThermodynamicTemperature = Dim Zero Zero Zero Zero Pos1 Zero Zero
type DAmountOfSubstance = Dim Zero Zero Zero Zero Zero Pos1 Zero
type DLuminousIntensity = Dim Zero Zero Zero Zero Zero Zero Pos1
type Dimensionless = Quantity DOne
type Length = Quantity DLength
type Mass = Quantity DMass
type Time = Quantity DTime
type ElectricCurrent = Quantity DElectricCurrent
type ThermodynamicTemperature = Quantity DThermodynamicTemperature
type AmountOfSubstance = Quantity DAmountOfSubstance
type LuminousIntensity = Quantity DLuminousIntensity
class Mul d d' d'' | d d' -> d''
class Div d d' d'' | d d' -> d''
class NumType x => Pow d x d' | d x -> d'
class NonZero x => Root d x d' | d x -> d'
(*) :: (Num a, Mul d d' d'') => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a
(/) :: (Fractional a, Div d d' d'') => Dimensional v d a -> Dimensional v d' a -> Dimensional v d'' a
(^) :: (Fractional a, Pow d n d') => Dimensional v d a -> n -> Dimensional v d' a
(^+) :: (Num a, PosType n, Pow d n d') => Dimensional v d a -> n -> Dimensional v d' a
negate :: Num a => Quantity d a -> Quantity d a
(+) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
(-) :: Num a => Quantity d a -> Quantity d a -> Quantity d a
abs :: Num a => Quantity d a -> Quantity d a
nroot :: (Floating a, Root d n d') => n -> Dimensional v d a -> Dimensional v d' a
sqrt :: (Floating a, Root d Pos2 d') => Dimensional v d a -> Dimensional v d' a
cbrt :: (Floating a, Root d Pos3 d') => Dimensional v d a -> Dimensional v d' a
(^/) :: (Floating a, Root d n d') => Dimensional v d a -> n -> Dimensional v d' a
(*~~) :: (Functor f, Num a) => f a -> Unit d a -> f (Quantity d a)
(/~~) :: (Functor f, Fractional a) => f (Quantity d a) -> Unit d a -> f a
sum :: Num a => [Quantity d a] -> Quantity d a
dimensionlessLength :: Num a => [Dimensional v d a] -> Dimensionless a
log :: Floating a => Dimensionless a -> Dimensionless a
sin :: Floating a => Dimensionless a -> Dimensionless a
cos :: Floating a => Dimensionless a -> Dimensionless a
tan :: Floating a => Dimensionless a -> Dimensionless a
asin :: Floating a => Dimensionless a -> Dimensionless a
acos :: Floating a => Dimensionless a -> Dimensionless a
atan :: Floating a => Dimensionless a -> Dimensionless a
sinh :: Floating a => Dimensionless a -> Dimensionless a
cosh :: Floating a => Dimensionless a -> Dimensionless a
tanh :: Floating a => Dimensionless a -> Dimensionless a
asinh :: Floating a => Dimensionless a -> Dimensionless a
acosh :: Floating a => Dimensionless a -> Dimensionless a
atanh :: Floating a => Dimensionless a -> Dimensionless a
exp :: Floating a => Dimensionless a -> Dimensionless a
(**) :: Floating a => Dimensionless a -> Dimensionless a -> Dimensionless a
atan2 :: RealFloat a => Quantity d a -> Quantity d a -> Dimensionless a
one :: Num a => Unit DOne a
_1 :: Num a => Dimensionless a
_2 :: Num a => Dimensionless a
_3 :: Num a => Dimensionless a
_4 :: Num a => Dimensionless a
_5 :: Num a => Dimensionless a
_6 :: Num a => Dimensionless a
_7 :: Num a => Dimensionless a
_8 :: Num a => Dimensionless a
_9 :: Num a => Dimensionless a
_0 :: Num a => Dimensionless a
pi :: Floating a => Dimensionless a
dimUnit :: NumType n => String -> n -> Maybe String
prefix :: Num a => a -> Unit d a -> Unit d a
instance Eq a => Eq (Dimensional v d a)
instance Ord a => Ord (Dimensional v d a)
instance (NumType l, NumType m, NumType t, NumType i, NumType th, NumType n, NumType j) => Show (Dim l m t i th n j)
instance (Show d, Show a) => Show (Quantity d a)
instance Functor Dimensionless
instance (Div l x l', Div m x m', Div t x t', Div i x i', Div th x th', Div n x n', Div j x j') => Root (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')
instance (Mul l x l', Mul m x m', Mul t x t', Mul i x i', Mul th x th', Mul n x n', Mul j x j') => Pow (Dim l m t i th n j) x (Dim l' m' t' i' th' n' j')
instance (Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Div (Dim l'' m'' t'' i'' th'' n'' j'') (Dim l' m' t' i' th' n' j') (Dim l m t i th n j)
instance (Sum l l' l'', Sum m m' m'', Sum t t' t'', Sum i i' i'', Sum th th' th'', Sum n n' n'', Sum j j' j'') => Mul (Dim l m t i th n j) (Dim l' m' t' i' th' n' j') (Dim l'' m'' t'' i'' th'' n'' j'')


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional.Quantities
type DArea = Dim Pos2 Zero Zero Zero Zero Zero Zero
type Area = Quantity DArea
type DVolume = Dim Pos3 Zero Zero Zero Zero Zero Zero
type Volume = Quantity DVolume
type DVelocity = Dim Pos1 Zero Neg1 Zero Zero Zero Zero
type Velocity = Quantity DVelocity
type DAcceleration = Dim Pos1 Zero Neg2 Zero Zero Zero Zero
type Acceleration = Quantity DAcceleration
type DWaveNumber = Dim Neg1 Zero Zero Zero Zero Zero Zero
type WaveNumber = Quantity DWaveNumber
type DMassDensity = Dim Neg3 Pos1 Zero Zero Zero Zero Zero
type MassDensity = Quantity DMassDensity
type Density = MassDensity
type DSpecificVolume = Dim Pos3 Neg1 Zero Zero Zero Zero Zero
type SpecificVolume = Quantity DSpecificVolume
type DCurrentDensity = Dim Neg2 Zero Zero Pos1 Zero Zero Zero
type CurrentDensity = Quantity DCurrentDensity
type DMagneticFieldStrength = Dim Neg1 Zero Zero Pos1 Zero Zero Zero
type MagneticFieldStrength = Quantity DMagneticFieldStrength
type DAmountOfSubstanceConcentration = Dim Neg3 Zero Zero Zero Zero Pos1 Zero
type AmountOfSubstanceConcentration = Quantity DAmountOfSubstanceConcentration
type Concentration = AmountOfSubstanceConcentration
type DLuminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1
type Luminance = Quantity DLuminance
square :: Num a => Unit DLength a -> Unit DArea a
cubic :: Num a => Unit DLength a -> Unit DVolume a
type DPlaneAngle = DOne
type PlaneAngle = Dimensionless
type DSolidAngle = DOne
type SolidAngle = Dimensionless
type DFrequency = Dim Zero Zero Neg1 Zero Zero Zero Zero
type Frequency = Quantity DFrequency
type DForce = Dim Pos1 Pos1 Neg2 Zero Zero Zero Zero
type Force = Quantity DForce
type DPressure = Dim Neg1 Pos1 Neg2 Zero Zero Zero Zero
type DStress = DPressure
type Pressure = Quantity DPressure
type Stress = Quantity DStress
type DEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Zero Zero
type DWork = DEnergy
type DQuantityOfHeat = DEnergy
type Energy = Quantity DEnergy
type Work = Quantity DWork
type QuantityOfHeat = Quantity DQuantityOfHeat
type DPower = Dim Pos2 Pos1 Neg3 Zero Zero Zero Zero
type DRadiantFlux = DPower
type Power = Quantity DPower
type RadiantFlux = Quantity DRadiantFlux
type DElectricCharge = Dim Zero Zero Pos1 Pos1 Zero Zero Zero
type DQuantityOfElectricity = DElectricCharge
type ElectricCharge = Quantity DElectricCharge
type QuantityOfElectricity = Quantity DQuantityOfElectricity
type DElectricPotential = Dim Pos2 Pos1 Neg3 Neg1 Zero Zero Zero
type DPotentialDifference = DElectricPotential
type DElectromotiveForce = DElectricPotential
type ElectricPotential = Quantity DElectricPotential
type PotentialDifference = Quantity DPotentialDifference
type ElectromotiveForce = Quantity DElectromotiveForce
type DCapacitance = Dim Neg2 Neg1 Pos4 Pos2 Zero Zero Zero
type Capacitance = Quantity DCapacitance
type DElectricResistance = Dim Pos2 Pos1 Neg3 Neg2 Zero Zero Zero
type ElectricResistance = Quantity DElectricResistance
type DElectricConductance = Dim Neg2 Neg1 Pos3 Pos2 Zero Zero Zero
type ElectricConductance = Quantity DElectricConductance
type DMagneticFlux = Dim Pos2 Pos1 Neg2 Neg1 Zero Zero Zero
type MagneticFlux = Quantity DMagneticFlux
type DMagneticFluxDensity = Dim Zero Pos1 Neg2 Neg1 Zero Zero Zero
type MagneticFluxDensity = Quantity DMagneticFluxDensity
type DInductance = Dim Pos2 Pos1 Neg2 Neg2 Zero Zero Zero
type Inductance = Quantity DInductance
type DLuminousFlux = DLuminousIntensity
type LuminousFlux = Quantity DLuminousFlux
type DIlluminance = Dim Neg2 Zero Zero Zero Zero Zero Pos1
type Illuminance = Quantity DIlluminance
type DCelsiusTemperature = DThermodynamicTemperature
type CelsiusTemperature = Quantity DCelsiusTemperature
type DActivity = DFrequency
type Activity = Quantity DActivity
type DAbsorbedDose = Dim Pos2 Zero Neg2 Zero Zero Zero Zero
type DSpecificEnergy = DAbsorbedDose
type DKerma = DAbsorbedDose
type AbsorbedDose = Quantity DAbsorbedDose
type SpecificEnergy = Quantity DSpecificEnergy
type Kerma = Quantity DKerma
type DDoseEquivalent = DAbsorbedDose
type DAmbientDoseEquivalent = DDoseEquivalent
type DDirectionalDoseEquivalent = DDoseEquivalent
type DPersonalDoseEquivalent = DDoseEquivalent
type DEquivalentDose = DDoseEquivalent
type DoseEquivalent = Quantity DDoseEquivalent
type AmbientDoseEquivalent = DoseEquivalent
type DirectionalDoseEquivalent = DoseEquivalent
type PersonalDoseEquivalent = DoseEquivalent
type EquivalentDose = DoseEquivalent
type DAngularVelocity = DFrequency
type AngularVelocity = Quantity DAngularVelocity
type DAngularAcceleration = Dim Zero Zero Neg2 Zero Zero Zero Zero
type AngularAcceleration = Quantity DAngularAcceleration
type DDynamicViscosity = Dim Neg1 Pos1 Neg1 Zero Zero Zero Zero
type DynamicViscosity = Quantity DDynamicViscosity
type DMomentOfForce = DEnergy
type MomentOfForce = Quantity DMomentOfForce
type DSurfaceTension = Dim Zero Pos1 Neg2 Zero Zero Zero Zero
type SurfaceTension = Quantity DSurfaceTension
type DHeatFluxDensity = Dim Zero Pos1 Neg3 Zero Zero Zero Zero
type DIrradiance = DHeatFluxDensity
type HeatFluxDensity = Quantity DHeatFluxDensity
type Irradiance = Quantity DIrradiance
type DRadiantIntensity = DPower
type RadiantIntensity = Quantity DRadiantIntensity
type DRadiance = DIrradiance
type Radiance = Quantity DRadiance
type DHeatCapacity = Dim Pos2 Pos1 Neg2 Zero Neg1 Zero Zero
type DEntropy = DHeatCapacity
type HeatCapacity = Quantity DHeatCapacity
type Entropy = Quantity DEntropy
type DSpecificHeatCapacity = Dim Pos2 Zero Neg2 Zero Neg1 Zero Zero
type DSpecificEntropy = DSpecificHeatCapacity
type SpecificHeatCapacity = Quantity DSpecificHeatCapacity
type SpecificEntropy = Quantity DSpecificEntropy
type DThermalConductivity = Dim Pos1 Pos1 Neg3 Zero Neg1 Zero Zero
type ThermalConductivity = Quantity DThermalConductivity
type DEnergyDensity = DPressure
type EnergyDensity = Quantity DEnergyDensity
type DElectricFieldStrength = Dim Pos1 Pos1 Neg3 Neg1 Zero Zero Zero
type ElectricFieldStrength = Quantity DElectricFieldStrength
type DElectricChargeDensity = Dim Neg3 Zero Pos1 Pos1 Zero Zero Zero
type ElectricChargeDensity = Quantity DElectricChargeDensity
type DElectricFluxDensity = Dim Neg2 Zero Pos1 Pos1 Zero Zero Zero
type ElectricFluxDensity = Quantity DElectricFluxDensity
type DPermittivity = Dim Neg3 Neg1 Pos4 Pos2 Zero Zero Zero
type Permittivity = Quantity DPermittivity
type DPermeability = Dim Pos1 Pos1 Neg2 Neg2 Zero Zero Zero
type Permeability = Quantity DPermeability
type DMolarEnergy = Dim Pos2 Pos1 Neg2 Zero Zero Neg1 Zero
type MolarEnergy = Quantity DMolarEnergy
type DMolarEntropy = Dim Pos2 Pos1 Neg2 Zero Neg1 Neg1 Zero
type DMolarHeatCapacity = DMolarEntropy
type MolarEntropy = Quantity DMolarEntropy
type MolarHeatCapacity = Quantity DMolarHeatCapacity
type DExposure = Dim Zero Neg1 Pos1 Pos1 Zero Zero Zero
type Exposure = Quantity DExposure
type DAbsorbedDoseRate = Dim Pos2 Zero Neg3 Zero Zero Zero Zero
type AbsorbedDoseRate = Quantity DAbsorbedDoseRate
type DImpulse = Dim Pos1 Pos1 Neg1 Zero Zero Zero Zero
type Impulse = Quantity DImpulse
type DMassFlow = Dim Zero Pos1 Neg1 Zero Zero Zero Zero
type MassFlow = Quantity DMassFlow
type DGravitationalParameter = Dim Pos3 Zero Neg2 Zero Zero Zero Zero
type GravitationalParameter = Quantity DGravitationalParameter
type Angle = PlaneAngle
type Thrust = Force
type EnergyPerUnitMass = SpecificEnergy


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional.SIUnits
deca :: Num a => Unit d a -> Unit d a
hecto :: Num a => Unit d a -> Unit d a
kilo :: Num a => Unit d a -> Unit d a
mega :: Num a => Unit d a -> Unit d a
giga :: Num a => Unit d a -> Unit d a
tera :: Num a => Unit d a -> Unit d a
peta :: Num a => Unit d a -> Unit d a
exa :: Num a => Unit d a -> Unit d a
zetta :: Num a => Unit d a -> Unit d a
yotta :: Num a => Unit d a -> Unit d a
deka :: Num a => Unit d a -> Unit d a
centi :: Fractional a => Unit d a -> Unit d a
milli :: Fractional a => Unit d a -> Unit d a
micro :: Fractional a => Unit d a -> Unit d a
nano :: Fractional a => Unit d a -> Unit d a
pico :: Fractional a => Unit d a -> Unit d a
femto :: Fractional a => Unit d a -> Unit d a
atto :: Fractional a => Unit d a -> Unit d a
zepto :: Fractional a => Unit d a -> Unit d a
yocto :: Fractional a => Unit d a -> Unit d a
deci :: Fractional a => Unit d a -> Unit d a
meter :: Num a => Unit DLength a
metre :: Num a => Unit DLength a
gram :: Fractional a => Unit DMass a
second :: Num a => Unit DTime a
ampere :: Num a => Unit DElectricCurrent a
kelvin :: Num a => Unit DThermodynamicTemperature a
mole :: Num a => Unit DAmountOfSubstance a
candela :: Num a => Unit DLuminousIntensity a
fromDiffTime :: Fractional a => DiffTime -> Time a
toDiffTime :: (Real a, Fractional a) => Time a -> DiffTime
radian :: Fractional a => Unit DPlaneAngle a
steradian :: Fractional a => Unit DSolidAngle a
hertz :: Fractional a => Unit DFrequency a
newton :: Fractional a => Unit DForce a
pascal :: Fractional a => Unit DPressure a
joule :: Fractional a => Unit DEnergy a
watt :: Fractional a => Unit DPower a
coulomb :: Fractional a => Unit DElectricCharge a
volt :: Fractional a => Unit DElectricPotential a
farad :: Fractional a => Unit DCapacitance a
ohm :: Fractional a => Unit DElectricResistance a
siemens :: Fractional a => Unit DElectricConductance a
weber :: Fractional a => Unit DMagneticFlux a
tesla :: Fractional a => Unit DMagneticFluxDensity a
henry :: Fractional a => Unit DInductance a
lumen :: Fractional a => Unit DLuminousFlux a
lux :: Fractional a => Unit DIlluminance a
degreeCelsius :: Num a => Unit DCelsiusTemperature a
fromDegreeCelsiusAbsolute :: Fractional a => a -> ThermodynamicTemperature a
toDegreeCelsiusAbsolute :: Fractional a => ThermodynamicTemperature a -> a
becquerel :: Fractional a => Unit DActivity a
gray :: Fractional a => Unit DAbsorbedDose a
sievert :: Fractional a => Unit DDoseEquivalent a
hour :: Num a => Unit DTime a
day :: Num a => Unit DTime a
minute :: Num a => Unit DTime a
arcminute :: Floating a => Unit DPlaneAngle a
arcsecond :: Floating a => Unit DPlaneAngle a
degree :: Floating a => Unit DPlaneAngle a
minuteOfArc :: Floating a => Unit DPlaneAngle a
secondOfArc :: Floating a => Unit DPlaneAngle a
degreeOfArc :: Floating a => Unit DPlaneAngle a
liter :: Fractional a => Unit DVolume a
litre :: Fractional a => Unit DVolume a
metricTon :: Fractional a => Unit DMass a
tonne :: Fractional a => Unit DMass a

module Numeric.Units.Dimensional.Prelude


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional.NonSI
electronVolt :: Fractional a => Unit DEnergy a
unifiedAtomicMassUnit :: Fractional a => Unit DMass a
gee :: Fractional a => Unit DAcceleration a
foot :: Fractional a => Unit DLength a
inch :: Fractional a => Unit DLength a
ounce :: Fractional a => Unit DMass a
poundMass :: Fractional a => Unit DMass a
poundForce :: Fractional a => Unit DForce a
psi :: Fractional a => Unit DPressure a
mile :: Fractional a => Unit DLength a
nauticalMile :: Fractional a => Unit DLength a
yard :: Fractional a => Unit DLength a
revolution :: Floating a => Unit DOne a
solid :: Floating a => Unit DOne a
teaspoon :: Fractional a => Unit DVolume a
century :: Num a => Unit DTime a
year :: Num a => Unit DTime a
bar :: Fractional a => Unit DPressure a
atmosphere :: Fractional a => Unit DPressure a
technicalAtmosphere :: Fractional a => Unit DPressure a
mmHg :: Fractional a => Unit DPressure a
torr :: Fractional a => Unit DPressure a
rad :: Fractional a => Unit DAbsorbedDose a


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional.Extensible
data DExt a n d
showDExt :: (NumType n, Show d) => String -> DExt a n d -> String
instance (Div n x n', Root d x d') => Root (DExt a n d) x (DExt a n' d')
instance (Mul n x n', Pow d x d') => Pow (DExt a n d) x (DExt a n' d')
instance (Sum n'' n' n, Div d d' d'', DropZero (DExt a n'' d'') d''') => Div (DExt a n d) (DExt a n' d') d'''
instance (Div (Dim l m t i th n j) d d', Negate x x') => Div (Dim l m t i th n j) (DExt a x d) (DExt a x' d')
instance Div d (Dim l m t i th n j) d' => Div (DExt a x d) (Dim l m t i th n j) (DExt a x d')
instance (Sum n n' n'', Mul d d' d'', DropZero (DExt a n'' d'') d''') => Mul (DExt a n d) (DExt a n' d') d'''
instance Mul (Dim l m t i th n j) d d' => Mul (Dim l m t i th n j) (DExt a x d) (DExt a x d')
instance Mul d (Dim l m t i th n j) d' => Mul (DExt a x d) (Dim l m t i th n j) (DExt a x d')
instance DropZero (DExt a (Neg n) d) (DExt a (Neg n) d)
instance DropZero (DExt a (Pos n) d) (DExt a (Pos n) d)
instance DropZero (DExt a Zero (DExt a' n d)) (DExt a Zero (DExt a' n d))
instance DropZero (DExt a Zero (Dim l m t i th n j)) (Dim l m t i th j j)


-- | Please refer to the literate Haskell code for documentation of both
--   API and implementation.
module Numeric.Units.Dimensional.CGS
data CGSDim lh mh t
type DLength = CGSDim Pos2 Zero Zero
type DMass = CGSDim Zero Pos2 Zero
type DTime = CGSDim Zero Zero Pos1
type DElectricCurrent = CGSDim Pos3 Pos1 Neg2
type DCharge = CGSDim Pos3 Pos1 Neg1
meter :: Num a => Unit DLength a
gram :: Num a => Unit DMass a
second :: Num a => Unit DTime a
ampere :: Floating a => Unit DElectricCurrent a
franklin :: Floating a => Unit DCharge a
unit_SI :: Num a => Quantity (Dim l m t i th n j) a -> Unit (Dim l m t i th n j) a
unit_CGS :: (Floating a, Mul Zero l Zero, Mul Pos2 l l2, Mul Zero m Zero, Mul Pos2 m m2, Mul Zero t Zero, Mul Pos1 t t, Sum l2 Zero l2, Sum Zero m2 m2, Sum m2 Zero m2, Sum Zero t t, Mul Pos3 i il, Mul Pos1 i i, Mul Neg2 i it, Sum l2 il l', Sum m2 i m', Sum t it t') => Quantity (Dim l m t i Zero Zero Zero) a -> Unit (CGSDim l' m' t') a
toSI :: (Floating a, Mul Zero l Zero, Mul Pos2 l l2, Mul Zero m Zero, Mul Pos2 m m2, Mul Zero t Zero, Mul Pos1 t t, Sum l2 Zero l2, Sum Zero m2 m2, Sum m2 Zero m2, Sum Zero t t, Mul Pos3 i il, Mul Pos1 i i, Mul Neg2 i it, Sum l2 il l', Sum m2 i m', Sum t it t') => Quantity (CGSDim l' m' t') a -> Quantity (Dim l m t i Zero Zero Zero) a
instance (NumType lh, NumType mh, NumType t) => Show (CGSDim lh mh t)
instance (Div lh x lh', Div mh x mh', Div t x t') => Root (CGSDim lh mh t) x (CGSDim lh' mh' t')
instance (Mul lh x lh', Mul mh x mh', Mul t x t') => Pow (CGSDim lh mh t) x (CGSDim lh' mh' t')
instance (Sum lh lh' lh'', Sum mh mh' mh'', Sum t t' t'') => Div (CGSDim lh'' mh'' t'') (CGSDim lh' mh' t') (CGSDim lh mh t)
instance (Sum lh lh' lh'', Sum mh mh' mh'', Sum t t' t'') => Mul (CGSDim lh mh t) (CGSDim lh' mh' t') (CGSDim lh'' mh'' t'')