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Is there some way to extend Mathematica's dimensional analysis? For example, I'd like to be able to provide it with dimensional equations like energy=mass with units scalings like c^2 and have it extend the possible interpretations in terms of target dimensions and/or units.

Although my question is more general, the aforementioned case is supported by DimensionalCombinations if you provide the additional parameter IncludeQuantities -> "PhysicalConstants" with this example:

DimensionalCombinations[
       { QuantityVariable["E", "Energy" ]},
       QuantityVariable["m", "Mass"],
     IncludeQuantities -> "PhysicalConstants",
     GeneratedParameters -> None]

which produces these possible interpretations: enter image description here

PS: I'm aware of this answer providing a kludge to extend units conversions but it isn't clear this will also extend the function of, for example, DimensionalCombinations and, in any event, I would hope for something that isn't a kludge. (And in any event, the code in that answer doesn't work on my cloud notebook copy. It produces an error upon executing the test.)

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    $\begingroup$ It isn't clear what you are looking for (also I don't see the connection to the post you linked to). Can you provide an example input that you would like to work but does not? $\endgroup$
    – Jason B.
    Commented Aug 30, 2022 at 17:40
  • $\begingroup$ I had the wrong link. Corrected. $\endgroup$ Commented Aug 30, 2022 at 17:53
  • $\begingroup$ BTW, there is a strong preference on SE for questions to be self-contained and not to depend on potentially volatile links to essential code. Folks seem okay with posting code to a permanent service like pastebin.com, if the code won't fit in a question. $\endgroup$
    – Michael E2
    Commented Aug 30, 2022 at 18:08
  • $\begingroup$ The code in that linked post is a horrible kludge because it tries to redefine internal functions that are bound to change - I would be very surprised if it still works after these years. Instead one should define their own function GeneralizedUnitConvert[....] which defaults to the usual UnitConvert when it has no special rules for the given inputs. $\endgroup$
    – Jason B.
    Commented Aug 30, 2022 at 18:39
  • $\begingroup$ Maybe these questions are related: Specify set of base units to use in UnitConvert, Getting useful units for combinations of physical constants like on WolframAlpha? $\endgroup$
    – Roman
    Commented Aug 30, 2022 at 20:15

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