Unable to convert $\TeX$ input into mathematica

Question

The input

ToExpression["\\sqrt{x y}", TeXForm]

gives me the $Failed output.

Maybe my very old computer is the problem, but that's the only command that has caused me problems, and that input is from the tutorials.

Answer 1

Edit

An updated version of this answer is here. I forgot that there was some duplication when I posted the linked answer, but the material in that answer is more recent so I'll update that one and leave this post unchanged.

End edit

The conversion from $\LaTeX$ in general is rather quirky, but I don't see a failure of the kind you see.

However, there is in fact something wrong: The $\LaTeX$ syntax you're entering is completely valid and it should be interpreted as the square root of the product of two variables, x and y. However, Mathematica (my version is 8.0.4) incorrectly outputs a single variable xy instead of a product.

So there is really a bug in how products are interpreted. The work-around is to put thin spaces in your $\LaTeX$ code explicitly, as in

ToExpression["\\sqrt{x\\,y}",TeXForm]

Now the question still is why your conversion failed. My only explanation for that would be that before executing the ToExpression, you might have had a global variable by the name xy defined in Mathematica, for which it turned out to be impossible to take the square root. You could test this by first typing Clear[xy,x,y] and then re-trying the conversion from $\LaTeX$.

Edit

To expand a little on the quirks of $\LaTeX$-to-Mathematica conversion, here are some more points to watch out for:

• To translate integrals properly, Mathematica expects the integration variable in the $\LaTeX$ code to be preceded by \\, d. Only with the additional space will it recognize the d as the differential part of the integral.
• Express derivatives using the \\partial symbol ($\partial$): ToExpression["\\frac{\\partial^2 f(x)}{\\partial x^2}", TeXForm, Hold]
• In the above code, the argument Hold prevents evaluation so you can copy the expression from the output cell if desired (you can later apply ReleaseHold to evaluate the expression)
• All matrices and vectors must be written in list form using escaped curly brackets, as in \\{x,y,f (z)\\}. The conversion of array environments or commands such as \pmatrix to Mathematica produces wrong formatting.
• To group expressions, use only round parentheses, i.e., \\left( and \\right), not square [...] or curly {...} brackets. The latter are interpreted differently by Mathematica.

I copied this list from this my web page where I also collected some notes on the reverse process of getting equations out of Mathematica.

Edit 2

A comment by RM below brings to mind another point that is related more to $\LaTeX$: some novice authors write lazy expressions like $volume = length \times area$ and wonder why the typeset equation has unnatural-looking character spacing inside the "words" used here as variables. The reason is that $\TeX$ considers each single character in a sequence such as volume to be a single variable and applies the corresponding horizontal spacing rules to them.

Not knowing this feature, you may think that Mathematica has every right to interpret x y and likewise xy as the name of a single variable "xy". However, that goes against the rules of the $\TeX$ language and is therefore an incorrect translation.