[Tex/LaTex] Smashoperator on two limits of sums

math-modemath-operatorsvertical alignment

Problem

This MWE with two sums, that have prolonged limits each:

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}

\begin{document}
    $\displaystyle x \wedge y =
    \sum_{1 \leq i_1 < \ldots < i_p \leq n}
    \sum_{1 \leq j_1 < \ldots < j_q \leq n}
    a_{i_1 \ldots i_p} b_{j_1 \ldots j_q}
    \; \underbrace{e_{i_1} \wedge \ldots \wedge e_{i_p} \wedge e_{j_1} \wedge \ldots \wedge e_{j_q}}_{\text{is sometimes 0}}$    
\end{document}

produces a lot of space for the sums. Nevertheless the readability is bad, as the limits are too close to each other. Usage of smashoperator{} will lead to an error and one limit not showing any more.
I would much prefer the second formula (or also additionally smashed on the left side of the first sum).

Question

How can I produce the second formula in the picture? (or any other nice looking 'smashed' result)

Edit

1) I found this (just the sums) code to be close to my desired result. However it yields an undefined control sequence error:

\smashoperator{\mathop{\smashoperator{\sum_{1 \leq i_1 < \ldots < i_p \leq n}\sum}}_{\qquad 1 \leq j_1 < \ldots < j_q \leq n}}

Best Answer

Maybe this? with a little help from \mathclap and stackengine. EDIT to replace \ldots with \dots and \cdots, per Mico's request. I hope I interpreted his request in the right way...

\documentclass{article}
\usepackage{amsmath}
\usepackage{mathtools}
\usepackage{stackengine}
\stackMath
\begin{document}
    $\displaystyle x \wedge y =\qquad
    \sum_{\mathclap{1 \leq i_1 < \dots < i_p \leq n}}\quad
    \sum_{\stackunder[5pt]{}{\scriptstyle\mathclap{1 \leq j_1 < \dots < j_q \leq n}}}
    a_{i_1 \dots i_p} b_{j_1 \dots j_q}
    \; \underbrace{e_{i_1} \wedge \cdots \wedge e_{i_p} \wedge e_{j_1} \wedge \cdots \wedge e_{j_q}}_{\text{is sometimes 0}}$    
\end{document}

Related Solutions

[Tex/LaTex] smashoperator overlaps big parentheses with limits

As noted in the comments, it's very difficult to define a \smashoperator command that deals with all possible cases involving long limits. To understand why it is difficult, you need to know a little about boxes in TeX. Roughly speaking, horizontally smashed boxes (the limits in this case) are considered to have zero width, and there is no easy way to say

Small objects should consider the limits to be smashed, but large objects should not.

which is what you need.

The following code seems to work in your case, but will probably fail in others that I have not considered. In my opinion it would be better to avoid long limits, because they are grotesque (perhaps this is why the author(s) of mathtools did not provide an easy way to construct them).

\documentclass{minimal}
\usepackage{mathtools}
\newcommand{\test}[4]{ %
  %
  \newbox\bigbox
  \newbox\smallbox
  \newbox\argbox
  \newdimen\smallwidth
  \newdimen\offsetwidth
  \newdimen\argwidth
  %
  %Store the unsmashed operator in \bigbox. 
  \sbox\bigbox{\ensuremath{\displaystyle #1_{#2}^{#3}}}
  %Now store the smashed operator in \smallbox. 
  \sbox\smallbox{\ensuremath{\smashoperator{#1_{#2}^{#3}}}}
  %Finally, store the argument in \argbox
  \sbox\argbox{\ensuremath{\displaystyle \,#4}}
  %Calculate the width of the argument
  \argwidth=\wd\argbox
  %
  %Calculate the width by which the limits protrude. Note:
  %this will evaluate to zero if the limits do not protrude.
  \offsetwidth=\wd\bigbox
  \smallwidth=\wd\smallbox
  \multiply\smallwidth by -1
  \advance\offsetwidth by \smallwidth
  \divide\offsetwidth by 2
  %
  %Place the unsmashed operator and the argument on the page, 
  %pulling back the argument by the appropriate distance.
  \usebox\bigbox\hspace{-\offsetwidth}\usebox\argbox
  %
  %If the width of the argument is less than the width of
  %the protrusion, we now need to add some more space.
  \ifnum\offsetwidth>\argwidth \hspace{\offsetwidth}\hspace{-\argwidth} \fi
  %
}
\begin{document}
\begin{equation*}
\left[\test{\bigcup}{longlimit}{longlimit}{f(x)} \right]
\quad
\left[\test{\bigcup}{veryverylonglimit}{veryverylonglimit}{f(x)} \right]
\quad
\left[\test{\bigcup}{x}{y}{f(x)} \right]
\end{equation*}
\end{document}

[Tex/LaTex] Limits under multiple \sum

Something like:

\mathop{\sum_{j=1}^{\infty}\sum_{k=1}^{\infty}}_{j>k}

maybe?

Looks like this:

enter image description here

Or if you want it on the same line as j=1 and k=1, then maybe:

\mathop{\sum^{\infty}\sum^{\infty}}_{j=1\ j>k\ k=1}