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:
  • GeneratedParametersChow 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:

In[1]:=
Click for copyable input
Out[1]=

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

In[2]:=
Click for copyable input
Out[2]=

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

In[3]:=
Click for copyable input
Out[3]=
Introduced in 2014
(10.0)