DimensionalCombinations

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

DimensionalCombinations[{pq1, pq2, ...}, dim] returns combinations matching dimensions of dim.

Examples

Find dimensionless combinations:

DimensionalCombinations[{QuantityVariable["l", "Length"], QuantityVariable["t", "Time"], QuantityVariable["v", "Speed"]}]

Match specific dimensions:

DimensionalCombinations[{QuantityVariable["m", "Mass"], QuantityVariable["v", "Speed"]}, QuantityVariable["e", "Energy"]]

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