Dimensions

Dimension

The dimension of a physical quantity.

The dimension is expressed as a collection $(a, b, c, d, e, f, g)$ of powers exponentiating each of the seven basic dimensions of the SI system,

\[\mathrm{M}^a \, \mathrm{L}^b \, \mathrm{T}^c \, \mathrm{I}^d \, \mathrm{\Theta}^e \, \mathrm{N}^f \, \mathrm{J}^g,\]

where

• $\mathrm{M}$: mass dimension
• $\mathrm{L}$: length dimension
• $\mathrm{T}$: time dimension
• $\mathrm{I}$: electrical current dimension
• $\mathrm{\Theta}$: temperature dimension
• $\mathrm{N}$: amount of substance dimension
• $\mathrm{J}$: luminous intensity dimension

Fields

• massExponent::Real: exponent $a$ of the mass dimension
• lengthExponent::Real: exponent $b$ of the length dimension
• timeExponent::Real: exponent $c$ of the time dimension
• currentExponent::Real: exponent $d$ of the electrical current dimension
• temperatureExponent::Real: exponent $e$ of the temperature dimension
• amountExponent::Real: exponent $f$ of the amount of substance dimension
• luminousIntensityExponent::Real: exponent $g$ of the luminous intensity dimension

Constructor

Dimension(; M::Real=0, L::Real=0, T::Real=0, I::Real=0, θ::Real=0, N::Real=0, J::Real=0)

Raises Exceptions

• Core.DomainError: if attempting to initialize any field with an infinite number

Remarks

The constructor converts any exponent to Int if possible.

Examples

Quantities describing an energy are of dimension

\[ \mathrm{M} \, \mathrm{L}^{2} \, \mathrm{T}^{-2}\]

The corresponding Dimension object is:

julia> Dimension(M=1, L=2, T=-2)
Dimension M^1 L^2 T^-2

Calling the constructor without any keyword arguments returns exponents that correspond to a dimensionless quantity:

julia> Dimension()
Dimension 1

Base.:*(number::Number, dimension::Dimension)
Base.:*(dimension::Dimension, number::Number)

Multiply each exponent in dimension by number.

If a quantity Q is of dimension D, then Q^p is of dimension p * D.

Example

Let us consider a quantity Q of dimension 'length':

julia> ucat = UnitCatalogue() ;

julia> Q = 2 * ucat.meter
2 m

julia> D = dimensionOf(Q)
Dimension L^1

If we raise Q to the power of 3, it has dimension $L^3$ which can be represented by 3 * D:

julia> D2 = dimensionOf(Q^3)
Dimension L^3

julia> D2 == 3 * D
true

Base.:*(dimension1::Dimension, dimension2::Dimension)

Add each exponent in dimension1 to its counterpart in dimension2.

If a quantity Q1 (Q2) is of dimension D1 (D2), then Q1 * Q2 is of dimension D1 * D2.

Example

julia> ucat = UnitCatalogue() ;

julia> Q1 = 2 * ucat.meter
2 m

julia> D1 = dimensionOf(Q1)
Dimension L^1

julia> Q2 = 3 / ucat.second
3 s^-1

julia> D2 = dimensionOf(Q2)
Dimension T^-1

julia> D = dimensionOf( Q1 * Q2 )
Dimension L^1 T^-1

julia> D == D1 * D2
true

Base.:/(dimension1::Dimension, dimension2::Dimension)

Subtract each exponent in dimension2 from its counterpart in dimension1.

If a quantity Q1 (Q2) is of dimension D1 (D2), then Q1 / Q2 is of dimension D1 / D2.

Example

julia> ucat = UnitCatalogue() ;

julia> Q1 = 2 * ucat.meter
2 m

julia> D1 = dimensionOf(Q1)
Dimension L^1

julia> Q2 = 3 / ucat.second
3 s^-1

julia> D2 = dimensionOf(Q2)
Dimension T^-1

julia> D = dimensionOf( Q1 / Q2 )
Dimension L^1 T^1

julia> D == D1 / D2
true

Base.inv(dimension::Dimension)

Invert a physical dimension.

If a quantity Q is of dimension D, then 1/Q is of dimension inv(D).

Base.:^(dimension::Dimension, exponent::Number)

Exponentiate a physical dimension.

If a quantity Q is of dimension D, then Q^p is of dimension D^p.

Base.:sqrt(dimension::Dimension)

Square root a physical dimension.

If a quantity Q is of dimension D, then sqrt(Q) is of dimension sqrt(D).

Base.:cbrt(dimension::Dimension)

Cubic root a physical dimension.

If a quantity Q is of dimension D, then cbrt(Q) is of dimension cbrt(D).