DimensionalCombinations
DimensionalCombinations[{pq1,pq2,…}]
returns the possible combinations of the list of physical quantities pqi that are dimensionless.
DimensionalCombinations[{pq1,pq2,…},dim]
returns the possible combinations of the list of physical quantities pqi that match the dimensions of physical quantity dim.
Details and Options
- Physical quantities can be valid QuantityVariable objects, "PhysicalQuantity" entities or physical quantity strings.
- dim can be a QuantityVariable object. It can also be a combination of QuantityVariable objects or their derivatives.
- Solutions are determined by the physical quantity components in unit dimensions purely mathematically and have no guarantee of physical significance.
- Physical dimensions include: "AmountUnit", "AngleUnit", "ElectricCurrentUnit", "InformationUnit", "LengthUnit", "LuminousIntensityUnit", "MassUnit", "MoneyUnit", "SolidAngleUnit", "TemperatureDifferenceUnit", "TemperatureUnit", and "TimeUnit".
- Dimensionless physical quantities will not be used in the solution.
- The following options can be given:
-
GeneratedParameters C how to name parameters that are generated IncludeQuantities {} additional quantities to include - GeneratedParameters takes the option None, which returns a list of parameter-free solutions.
- IncludeQuantities allows quantity values and constants to be included in the combinations.
- The setting "PhysicalConstants" for IncludeQuantities includes the quantities Quantity["BoltzmannConstant"], Quantity["ElectricConstant"], Quantity["GravitationalConstant"], Quantity["MagneticConstant"], Quantity["PlanckConstant"], and Quantity["SpeedOfLight"].
Examples
open all close allBasic Examples (1)
Scope (3)
Use any combination of QuantityVariable objects or physical quantity strings:
The target physical dimensions can be specified as a combination of physical quantities:
Derivative objects may also be included in the expression:
"PhysicalQuantity" entities, including in QuantityVariable expressions, can also be used:
Options (5)
GeneratedParameters (3)
Use a different symbol for parameters:
By default, a generic solution is returned:
Use GeneratedParameters->None to get specific solutions:
GeneratedParameters->None works with IncludeQuantities to allow mixtures of QuantityVariable and Quantity objects:
IncludeQuantities (2)
Include additional constants and Quantity objects in the result:
Use the setting "PhysicalConstants" to include a standard set of physical constants:
Applications (4)
Find the missing physical constants in the formula E^2 - p^2 == m^2:
Solve for the value of the constants:
Eliminate unnecessary constants:
Find the dimensions of the constant needed to balance Kleiber's law 
:
Solve for the value of the mass exponent:
Estimate the power of a bomb blast by using only these physical quantities:
Construct a dimensionless combination:
Given the values of the parameters at a given time, estimate the energy of an explosion:
Determine possible dimensionless price impact functions depending on stock price, size and cost of bets, trading volumes and the volatility of the stock:
Properties & Relations (1)
Possible Issues (5)
Only valid physical quantities can be used:
Dimensionless quantities will be omitted from the result:
Only valid constants will be used:
Angular units and physical quantities are not treated as dimensionless:
While returned combinations are dimensionless, they do not necessarily have a magnitude of one:
Interactive Examples (1)
Text
Wolfram Research (2014), DimensionalCombinations, Wolfram Language function, https://reference.wolfram.com/language/ref/DimensionalCombinations.html (updated 2018).
CMS
Wolfram Language. 2014. "DimensionalCombinations." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2018. https://reference.wolfram.com/language/ref/DimensionalCombinations.html.
APA
Wolfram Language. (2014). DimensionalCombinations. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DimensionalCombinations.html