Using $1over2$ instead of $frac{1}{2}$ under amsmath

Question

I know that you should use $frac{1}{2}$ instead of $1over2$ to prevent warnings when you're using amsmath. But do those two expressions print differently? I know why, according to the amsmath technical notes, the over syntax was probably not the best one for TeX to use, but currently, does $frac{1}{2}$ have any capabilities that $1over2$ doesn't have?
If a person wrote an article using amsmath and over throughout, would there be any gain in changing all the over's to frac's?

David Carlisle · Accepted Answer

It prints the same: frac is defined in terms of over (or rather @@over which is the saved primitve) but you would feel better for doing the right thing if you use frac.

egreg · Answer

I see no advantage in using over instead of frac.

Moreover, $frac{1}{2}$ and $1over2$ are different. See the output of texdef -t latex frac:

frac:
macro:#1#2->{begingroup #1endgroup over #2}

You can see two things: first an additional set of braces around the fraction and then a “semisimple group” around the numerator.

Let me explain the difference.

The semisimple group around the numerator avoids some glitches that can make assignments meant to hold in the numerator only also in the denominator.
The group around the fraction avoids problems in the syntax.

If you type $1+1over2$ or $1+{1over2}$ you get different results; with $frac{1+1}{2}$ and $1+frac{1}{2}$ you're sure about what gets where.

I'm not alone in thinking that this is one of the worst design decision made by Knuth about math typesetting; with the over syntax you can't predict the math style used in the two parts of the fraction.

The amsmath package adds another layer, making frac robust, so it gets unchanged in moving arguments. It also adds the warning about the “foreign command”.

Dr. Manuel Kuehner · Answer

In the famous l2tabu document which collects 'sins' you can read on page 11

Der Befehl over sollte vermieden werden. over ist ein TeX-Befehl, der durch die von
      LaTeX abweichende Syntax schlechter beziehungsweise nicht parsbar ist. Insbesondere
      das Paket amsmath.sty definiert frac{}{} um, und man erhält Fehlermeldungen bei
      der Verwendung von over. Ein weiteres Argument für die Verwendung von frac{}{}
      ist die für den Benutzer – vorallem bei komplexeren Brüchen – einfachere Zuordnung
      von Zähler und Nenner.

This is German and means basically that over is a TeX command that could have some issues using LaTeX (something about parsing - but this exceeds my LaTeX skills). In addition frac{}{} is clearer and easier to read especially when you are typesetting complex equations.

There is also an English  version of the document but it is very old (2007) compared to the German version (2011).

Using $1over2$ instead of $frac{1}{2}$ under amsmath

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