Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

DimensionalCombinations

DimensionalCombinations[{pq1,pq2,}]
returns the possible combinations of the list of physical quantities that are dimensionless.

DimensionalCombinations[{pq1,pq2,},dim]
returns the possible combinations of the list of physical quantities that match the dimensions of physical quantity dim.

Details and OptionsDetails and Options

• Physical quantities can be valid QuantityVariable objects 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: , , , , , , , , , , , and .
• 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 for IncludeQuantities includes the quantities Quantity["BoltzmannConstant"], Quantity["ElectricConstant"], Quantity["GravitationalConstant"], Quantity["MagneticConstant"], Quantity["PlanckConstant"], and Quantity["SpeedOfLight"].

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Determine the combination of physical quantities that are dimensionally equivalent to energy:

 Out[1]=

Find all combinations of physical quantities that result in a dimensionless expression:

 Out[2]=

Discover if a dimensionless expression is possible with a set of physical quantities:

 Out[3]=