# UnitConvert of a Quantity whose value is a function of a Quantity

I am having trouble with UnitConvert when the QuantityMagnitude contains an embedded Quantity of its own. Here's an example of what happens, read on for my specific application. I would expect the last two outputs to be equal, but they are not.

Input:

Quantity[f[Quantity[x, "Meters"]], "Seconds"]
UnitConvert[%, "Hours"]
QuantityMagnitude[%] // FullForm
%[[2, 1]]
UnitConvert[%, Quantity["Feet"]]
UnitConvert[Quantity[x, "Meters"], Quantity["Feet"]]


Output:

f[x m] s
f[Quantity[x,CalculateUnitsUnitCommonSymbolsMeters]]/3600 h
Times[Rational[1,3600],f[Quantity[x,CalculateUnitsUnitCommonSymbolsMeters]]]
Quantity[x,CalculateUnitsUnitCommonSymbolsMeters]
UnitConvert[Quantity[x,CalculateUnitsUnitCommonSymbolsMeters],1 ft]
(1250 x)/381 ft


I have a rule defined to work on only Quantity parameters of the correct units, like so, which does some basic unit conversion and passes its magnitude to a numeric function:

f[Quantity[x_, ("Meters")^-1]] :>
f2[QuantityMagnitude@
UnitConvert[Quantity[x, ("Meters")^-1], ("Angstroms")^-1]]


The result is dimensionless (f2 is looking up a ratio at some physics wavenumber).

I then multiply that dimensionless result by a Quantity with complicated units for a later calculation. I can simplify the complicated units using UnitConvert, which can only be done if the whole expression is a Quantity, so I bring the f[x] inside to multiply the value of the complicated units (see my earlier question here). But when I try to simplify the complicated units using UnitConvert, it replaces the "Meters" unit with the symbol

CalculateUnitsUnitCommonSymbolsMeters


which I suspect is never meant to be seen. In any case, the Quantity that it is a part of no longer works as a regular Quantity with functions like UnitConvert or even QuantityMagnitude.

Is this a bug? What can I do to work around it?

• In Mathematica 10.0.2.0, the last two outputs are equal. More specifically: I do not see the CalculateUnitsUnitCommonSymbolsMeters anywhere in my output. Which version are you using? Maybe you need to try it in a new Mathematica session to avoid possibly conflicting definitions elsewhere. Mar 11 '15 at 6:39

I get that same odd result w/v9

you might try something like this as a workaround..

 unitConvert[Quantity[mag_, unit_], tounit_] :=
Quantity[ QuantityMagnitude[#]  mag  ,
QuantityUnit[#] ] &@ UnitConvert[Quantity[1, unit], tounit]

unitConvert[Quantity[f[Quantity[x, "Meters"]], "Seconds"], "Hours"]


Quantity[f[Quantity[x, "Meters"]]/3600, "Hours"]

• Yes, I'm using 9.0.2, so I suppose it is a bug that's been fixed in 10. That work around works well enough, just a shame that it needs to be used. Mar 12 '15 at 3:54