bugs - How do I prevent Mathematica from reformatting the expressions that I copy as LaTeX?

When I choose something that looks like

$$ W_1(1)=\rho ^{5} \omega _1 \rho ^{-5}\\ W_2(2)=\rho ^{23} \omega _2 \rho ^{-23}\\ W_3(3)=\rho ^{10} \omega _3 \rho ^{-10}\\ W_4(4)=\rho ^{9} \omega _4 \rho ^{-9} $$

in Mathematica and select Copy As > LaTeX I get something entirely different:

$$ W_1(1)=\frac{\rho ^5 \omega _1}{\rho ^5}\\ W_2(2)=\frac{\rho ^{23} \omega _2}{\rho ^{23}}\\ W_3(3)=\frac{\rho ^{10} \omega _3}{\rho ^{10}}\\ W_4(4)=\frac{\rho ^9 \omega _4}{\rho ^9} $$

How do I prevent Mathematica from reformatting the expressions that I copy as LaTeX?

Answer

Unfortunately, the Mathematica's Copy As > LaTeX command is not (as you'd expect) a command that copies the selected expressions as LaTeX. Instead, it performs additional reformatting that can only be avoided by changing behavior of the relevant built-in function with:

System`FEDump`CopyAsTeXMakeBoxes = #&

---

Details

Why copied boxes are reformatted

Copy As > LaTeX command, under the hood, calls FrontEnd`CopyAsTeX function.

If we spelunk it:

Import["https://raw.githubusercontent.com/szhorvat/Spelunking/master/Spelunking.m"]
Spelunk@FrontEnd`CopyAsTeX

we'll see it performs several steps. Relevant, for answer to this question, is call to System`FEDump`TransformBoxesToTraditionalFormBoxes function. We can "discover" it using pop-up that appears after clicking on this function's name.

We'll see that, basically, it calls MakeExpression[..., "StandardForm"] on given boxes, than passes resulting expression to System`FEDump`CopyAsTeXMakeBoxes function, together with boxes. CopyAsTeXMakeBoxes function calls MakeBoxes[..., "TraditionalForm"] on given expression.

This is the place where reformatting occurs.

If we take expression from question and pass it, converted to boxes, to TransformBoxesToTraditionalFormBoxes we'll get:

HoldForm[Equal[Subscript[W,1][1],Times[Power[ρ,5],Subscript[ω,1],Power[ρ,Times[-1,5]]]]] // MakeBoxes
System`FEDump`TransformBoxesToTraditionalFormBoxes[%]
(* TagBox[RowBox[{RowBox[{SubscriptBox[W,1],(,1,)}],==,FractionBox[RowBox[{SuperscriptBox[ρ,5], ,SubscriptBox[ω,1]}],SuperscriptBox[ρ,5]]}],HoldForm] *)
% // DisplayForm

$W_1(1)=\frac{\rho ^5 \omega _1}{\rho ^5}$

We see that HoldForm TagBox is still there. TransformBoxesToTraditionalFormBoxes and CopyAsTeXMakeBoxes are written in safe way, there's no evaluation leak. Expression created from boxes is wrapped with HoldComplete and function applied to it has properly set HoldAllComplete attribute. Reformatting is done purely by MakeBoxes function.

TransformBoxesToTraditionalFormBoxes was added in Mathematica version 9. Verison 8 copies expressions without reformatting.

How to change Copy As > LaTeX behavior

System`FEDump`CopyAsTeXMakeBoxes takes two arguments first are (almost) original boxes, second is expression obtained from those boxes. Original boxes are returned when reconverting expression to boxes encounters any problems.

If we don't mind changing behavior of built-in function, we can force CopyAsTeXMakeBoxes to always return unchanged boxes by setting:

System`FEDump`CopyAsTeXMakeBoxes = #&

Solution tested in Mathematica versions 9 and 10. Previous versions don't need it.