Latex - superscript & subscript together

[csopi]

latex -- superscript & subscript together

Hi,

I need to use expressions that have arguments, multiple superscript and subscript indices at the same time, e.g

$$V(ij)_{\sigma_1\sigma_2}^{\tau_1\tau_2}$$

Is it possible to force latex to make this formula more compact, ie. to put the sigma and tau indices right after V, above / below (ij)?

Thanks for your help!

 

[Simon Bridge]

Something like this:
$$\underset{\sigma_1 \sigma_2}{\overset{\tau_1 \tau_2}{V_{i,j}}}$$If you need to do it a lot, you'll want to define a new command:

\newcommand{\vc}[3]{\overset{#2}{\underset{#3}{#1}}}

... the use would be \vc{bace}{over}{under}

\vc{X}{a,b}{c,d}$$\newcommand{\vc}[3]{\overset{#2}{\underset{#3}{#1}}} \vc{X}{a,b}{c,d}$$

 

[csopi]

Thank you very much, that is really nice! Is it possible to put them to the top right / bottom right corner of V?

 

[Simon Bridge]

They are at the top-right/bottom-right corners of the V... well the start there.
You want them to end there?
Well ... using _a^bV^c_d:$$_a^bV^c_d$$... or \sideset{_a^b}{_d^c}V$$\sideset{_a^b}{_d^c}V$$... hmmm, pretty much the same (bit more square).$$\overset{\tau_1 \; \tau_2}{\underset{\sigma_1 \; \sigma_2}{V_{i,j}}}$$... expoits the centering by adding a horizontal space. I can make it wider:$$\overset{\tau_1 \;\; \tau_2}{\underset{\sigma_1 \;\; \sigma_2}{V_{i,j}}}$$... nesting the subscripts is pretty messy though.

Try looking through ftp://ftp.ams.org/pub/tex/doc/amsmath/short-math-guide.pdf for more possibilities.

 

[Borek]

That's what I was looking for not long ago...

$$C \iiint^{+\infty}_{-\infty}e^{-\frac \beta {2m} (p^2_x+p^2_y+p^2_z)}dp_x dp_y dp_z = 1$$

$$C \underset{-\infty}{\overset{+\infty} \iiint} e^{-\frac \beta {2m} (p^2_x+p^2_y+p^2_z)}dp_x dp_y dp_z = 1$$

Still not perfect, but already better.

 

[D H]

That's what I was looking for not long ago...

$$C \iiint^{+\infty}_{-\infty}e^{-\frac \beta {2m} (p^2_x+p^2_y+p^2_z)}dp_x dp_y dp_z = 1$$

$$C \underset{-\infty}{\overset{+\infty} \iiint} e^{-\frac \beta {2m} (p^2_x+p^2_y+p^2_z)}dp_x dp_y dp_z = 1$$

Still not perfect, but already better.

That first one looks like a pair of indefinite integrals over a definite integral. The latter is rather non-standard.

What you are trying to say is that you want to integrate over all of momentum space (I assume p is some generalized momentum). There's nothing wrong with $\iiint_V f(V)\,dV$, where V is the volume to be integrated over. Using $\iiint_V f(x,y,z)\,dx\,dy\,dz$ is perhaps an abuse of notation, but it is a widely used and widely understood abuse of notation. Your momentum space is ℝ³. So just say so:

$$C \iiint_{\mathbb R^3}e^{-\frac \beta {2m} (p^2_x+p^2_y+p^2_z)}dp_x dp_y dp_z = 1$$

 

[csopi]

Thank you Simon, I really appreciate your help!

 

[Borek]

The latter is rather non-standard.

That's the way it was shown in the Physical Chemistry textbook printed here many times since at least seventies and considered for many years to be a standard text (called "a brick" for the size, weight, and cover color). Doesn't make it correct, it is just not something I made up - rather something I selected for aesthetic reasons.

 

[Simon Bridge]

@csopi: no worries.

@D_H: I have also seen:$$\underset{\infty}{\iiint}f(x,y,z)dxdydz$$... as a shorthand for integrating over all space. Sometimes not even a triple-int sign. It may even be $$\underset{\infty}{\int}Fd\tau$$... so these things are used whatever we may think of them.
I mostly associate this sort of thing with the preliminary notes in a handwritten document.

Sometimes it looks tidier to write$$\underset{-\infty}{\int}^\infty f(x)dx$$... but I'm like: "meh": it looks ugly with pretty much anything else.