# Correct symbol for the Laplace operator ($\Delta$)

What is the correct symbol to use for the Laplace operator? It looks almost like the big Delta $\Delta$, but it should look different so that it is not confused with the Delta.

Currently, I use $\vec \nabla^2$, which is unambiguous, but not pretty.

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According to the Comprehensive LaTeX Symbol List \Delta is used for it. See page 50. – azetina Oct 13 '12 at 18:07
Also, the only symbol used on Wikipedia - the source of all knowledge - is \Delta (apart from \mathcal{L}). :) – Werner Oct 13 '12 at 18:16
Link to Comprehensive LaTeX Symbol List. See page 50. – azetina Oct 13 '12 at 18:17
don't you mean page 150, @azetina? Page 50 has only arrows. – c.p. Oct 13 '12 at 18:22
Even if they look different, they will be confused. Don't use them with different meanings! (The same applies, e.g., to \epsilon and \varepsilon.) – Hendrik Vogt Oct 13 '12 at 19:23

If you use the D'Alembert operator as well, you might find pretty using the symbol \bigtriangleup for your Laplace operator, in order to get a similar look as the \Box symbol that is being used for D'Alambertian. In the following, a tricky construction with \mathop and \mathbin is used to get the proper spacing:

\documentclass{article}

\usepackage{amsmath,amssymb}

\newcommand*\Laplace{\mathop{}\!\mathbin\bigtriangleup}
\newcommand*\DAlambert{\mathop{}\!\mathbin\Box}

\pagestyle{empty}

\begin{document}

\begin{gather*}
\phi(1+\Laplace A) \neq \phi(1+\Delta A)
\\
\phi(1+\DAlambert A) \neq \phi(1+\Laplace A)
\\
f\Laplace g
\end{gather*}

\end{document}


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I'd use \mathop{{}\bigtriangleup}\nolimits and \mathop{{}\Box}\nolimits which would ensure correct spacing in all situations. The {} is in order to avoid centering the operator with respect to the formula axis. – egreg Oct 13 '12 at 21:15
The d'Alambert operator will come eventually since I am a physicist. I like your solution, since it looks consistent. – Martin Ueding Oct 14 '12 at 14:29

The operator is defined, in the international standard ISO 80000-1, as identified with the Unicode character U+2206 INCREMENT (mistakenly called DELTA in the standard), which has “Laplace operator” as one of its alias names. Thus, it is regarded as distinct from the Greek capital letter delta U+0394. This is however a logical, character-level distinction and does not imply that different glyphs must be used. On the other hand, many fonts make a distinction, sometimes very small, sometimes quite noticeable.

It seems to me that to make the difference in LaTeX, you would need to use a package that lets you enter a character by its Unicode number or enter Unicode characters as such. Along that second option, the following code seems to produce different renderings:

\documentclass{article}
\usepackage{unicode-math}
\setmathfont{XITS Math}
\begin{document}
U+2206: $∆$

U+0394: $Δ$
\end{document}


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I've taken the liberty of modifying your example; first to use XITS Math which is the same as STIXGeneral, but doesn't raise warnings when used as a math font. The other change is for making clear what Unicode character produces each glyph. – egreg Oct 13 '12 at 21:19
@egreg: Could you please add a possibility to define a command for the "U+2206". I would like to get a "\laplace" working with lualatex and \usepackage[math-style=ISO]{unicode-math}. Thanks! – LaRiFaRi Sep 2 '13 at 15:31
@LaRiFaRi The symbol is called \increment with unicode-math. If you want \laplace to use it, just do \newcommand{\laplace}{\increment} – egreg Sep 2 '13 at 15:40
It seems that unfortunately the package unicode-math requires one of the compilers xelatex or Lualatex. – strpeter Oct 30 '13 at 14:58

According to the Comprehensive LaTeX Symbol List one can use the symbol \Delta and corresponding \nabla to represent the Laplace operator.

I don't know if \Updelta is a possibility from txfonts/pxfonts.

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