[Tex/LaTex] How to type tensor multiplication with vertical dots

symbolstensor

I want to type this equation in LaTeX. How do I type those vertical dots symbol?

Best Answer

These are obviously binary operators, so they should carry the same spacing. That is, use whatever works and then wrap it in \mathbin. While the original picture showed the bottom dots resting on the baseline, I think it would be more correct to center the symbols on the math axis (where the \cdot is placed). Here is a simple possibility, that does not allow for size changes in scripts, but does respect global size changes like \large.

\documentclass{article}

\def\onedot{$\mathsurround0pt\ldotp$}
\def\cddot{% two dots stacked vertically
  \mathbin{\vcenter{\baselineskip.67ex
    \hbox{\onedot}\hbox{\onedot}}%
  }}%
\def\cdddot#1{% three dots 
  \mathbin{\vcenter{\baselineskip.67ex
    \hbox{\onedot}\hbox{\onedot}\hbox{\onedot}%
  }}%
}

\begin{document}
Test it:
\[
\mathbf{P} = \varepsilon_0 \left(\chi^{(1)}
    \cdot \mathbf{E} + \chi^{(2)}
    \cddot \mathbf{EE} + \chi^{(3)}
    \cdddot \mathbf{EEE} + \cdots \right)
\]
\end{document}

Allowing for changes in scripts is a good deal harder, but could be done with the aid of some of the internals of the mathdots package.

Related Solutions

[Tex/LaTex] Symbols for four and five vertical dots

Here's one way. The gap is controlled by the \setstackgap macro; The whole thing can be raised or lowered with a \raisebox; the number of dots in the stack are the space-separated argument of the stack.

Note: you could stack any characters as such, not just dots. If the [usestackEOL] option is passed to the package, the EOL separator is no longer a space, but a \\ character.

\documentclass{article}
\usepackage{stackengine}
%\stackMath
\setstackgap{S}{1pt}
\begin{document}
$A \Shortstack{. . . .}B$
$A \raisebox{-1.2pt}{\Shortstack{. . . . .}}B$
$A \setstackgap{S}{.5pt}\Shortstack{. . . . .}B$
\end{document}

enter image description here

[Tex/LaTex] Vertical dots with same height as colon

If you want a version of \vdots that is exactly as tall as a colon you could try to overlay a \cdot on top of a :. The code below, which is based on this excellent answer, does exactly this.

I'm actually defining several different versions of \threedots with different spacing properties:

\threedotsord has the same spacing as ordinary letters;
\threedotsopen and \threedotsclose have the same spacing as opening and closing parentheses respectively;
\threedotsbin has the same spacing as a binary operator (like +, -, \times,…);
\threedotsrel has the same spacing as a relation symbol (like =, <, \sim, \rightorrow, …).

Which version you need will depend on how you intend to use the symbol. Since you're talking about operator ordering, you will probably want to use \threedotsopen and \threedotsclose. For convenience, I defined a macro \oporder that puts a pair of triple dots with the correct spacing around its argument.

\documentclass{article}

\makeatletter %% <- make @ usable in macro names
\newcommand*\superimpose[2]{%
  \ooalign{$\m@th#1\@firstoftwo#2$\cr
           \hidewidth$\m@th#1\@secondoftwo#2$\hidewidth}%
}
\makeatother %% <- revert @

%% You may want to rename these...
\newcommand*\threedotsord{\mathpalette\superimpose{{\mathop:}{\cdot}}} %% <- normal
\newcommand*\threedotsopen{\mathopen{\threedotsord}}   %% <- spacing like (
\newcommand*\threedotsclose{\mathclose{\threedotsord}} %% <- spacing like )
\newcommand*\threedotsbin{\mathbin{\threedotsord}}     %% <- spacing like +, -, ...
\newcommand*\threedotsrel{\mathrel{\threedotsord}}     %% <- spacing like =, <, ...

\newcommand*\oporder[1]{\threedotsopen#1\threedotsclose} %% <- wraps argument in these

\begin{document}

Using the \verb|\mathopen| and \verb|\mathclose| versions is probably what you want:
\[
    1 + \oporder{ x(t_1) x(t_2) x(t_3) } + \delta
\]

The spacing is nearly always the same as for ordinary atoms though:
\[
    1 + \threedotsord x(t_1) x(t_2) x(t_3) \threedotsord + \delta
\]

Using \verb|\mathbin| or \verb|\mathrel| would be wrong in this context:
\[
    1 + \threedotsbin x(t_1) x(t_2) x(t_3) \threedotsbin + \delta
\]
\[
    1 + \threedotsrel x(t_1) x(t_2) x(t_3) \threedotsrel + \delta
\]

This also works in superscripts and subscripts
\[
    X_{\oporder{xyz}^{\oporder{abc}}}
\]

\end{document}

Note that \mathop vertically centres its argument with respect to the math axis whenever it is applied to a single character, as remarked e.g. here. You could also centre the \cdot with respect to the :, but this is more work (if you want to do it automatically, without guessing the amount to lower it by).

Best Answer

Related Solutions

[Tex/LaTex] Symbols for four and five vertical dots

[Tex/LaTex] Vertical dots with same height as colon

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