Intended behavior for dimension errors on SymbolicDimensions

[MilesCranmer]

I would like to hear the opinions of @odow @trulsf for JuMP and maybe @ChrisRackauckas or @YingboMa for ModelingToolkit.jl.

What would you prefer the behavior to be when you try to add two quantities that have incompatible SymbolicDimensions?

First, recall that SymbolicDimensions is a way to avoid automatically converting to SI base units:

For example:

julia> q = 4us"kPa * Constants.c"
4.0 kPa c

julia> sqrt(q)
2.0 kPa¹ᐟ² c¹ᐟ²

Only when you call expand_units would it convert from SymbolicDimensions to Dimensions:

julia> expand_units(q)
1.199169832e12 kg s⁻³

Right now when you try to add two incompatible quantities, the behavior is:

julia> 1us"km/s" + 1us"m/s"
ERROR: DimensionError: 1.0 s⁻¹ km and 1.0 m s⁻¹ have incompatible dimensions

whereas with regular Dimensions, you get:

julia> 1u"km/s" + 1u"m/s"
1001.0 m s⁻¹

Questions for you: is this behavior good as-is? Or should there be some way to automatically convert to SI units when this happens, but stay in SymbolicDimensions (to avoid type instability)?

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Another option would be to perform all computations with Dimensions, and then display by converting back to SymbolicDimensions. For example:

julia> output_units = us"km/hr";

julia> a = 15us"km/hr"; b = 30us"m/s";

julia> raw_output = expand_units(a) + expand_units(b)
34.166666666666664 m s⁻¹

julia> as_units(q, units) = Quantity(ustrip(q / expand_units(units)) * ustrip(units), dimension(units));

julia> as_units(raw_output, output_units)
122.99999999999999 km hr⁻¹