Changing every operator in a document

Question

I'm writing notes on vector calculus and have been using the \curl and \div operators from the physics package. Only after a while did I realise that \curl uses the bold-face version of \nabla rather than just \nabla.

Initially, I wanted to make all the bold-face nablas the same as the standard nablas, and managed to do that with this (from this post):

\DeclareDocumentCommand\vnabla{}{\nabla}

However, I think I actually like the bold-face version better and want to change all the existing nablas in the document to bold-face, preferably by redefining \nabla to produce the bold-face version (rather than manually searching for every single nabla in the document).

How would I do this? Sorry if this question is elementary. Any advice would be appreciated.

Answer 1

The \nabla command is defined as a character, using \mathchardef so to redefine it as a macro you need to create a new version of it that can be made bold in the same way that the physics package defines the \vnabla macro.

\documentclass{article}
\usepackage{physics}
\mathchardef\NABLA"272
\newcommand*{\Nabla}{\boldsymbol\NABLA}
\let\nabla\Nabla
\begin{document}
\[ \nabla(\frac{a}{b}) \]
\[ \grad(\frac{a}{b}) \]
\end{document}

Answer 2

You want to keep the standard \nabla somewhere and redefine the command, in order to avoid an infinite loop.

\documentclass{article}
\usepackage{amsmath,bm}

\AtBeginDocument{%
  \NewCommandCopy{\nablasymbol}{\nabla}%
  \DeclareRobustCommand{\nabla}{\bm{\nablasymbol}}%
}

\begin{document}

$\nabla$ (compare with $\nablasymbol$)

\end{document}

Note that you need to know nothing about how \nabla is defined to begin with. Also, \AtBeginDocument might be necessary if you use one of the math font packages that delay definitions at begin document; it doesn't harm doing it anyway.

If you're using unicode-math, the method is similar.

\documentclass{article}
\usepackage{amsmath}
\usepackage{unicode-math}

\AtBeginDocument{%
  \NewCommandCopy{\nablasymbol}{\nabla}%
  \DeclareRobustCommand{\nabla}{\symbf{\nablasymbol}}%
}

\begin{document}

$\nabla$ (compare with $\nablasymbol$)

\end{document}

Here \AtBeginDocument is certainly needed, because unicode-math does much of its job at that moment and we must delay the redefinition after that job.

Answer 3

If you are using Unicode math then all variants of nabla are ready in single font. Looking to unicode-math-table.tex we get:

\UnicodeMathSymbol{"02207}{\nabla          }{\mathalpha}{nabla, del, hamilton operator}%
\UnicodeMathSymbol{"1D6C1}{\mbfnabla       }{\mathalpha}{mathematical bold nabla}%
\UnicodeMathSymbol{"1D6FB}{\mitnabla       }{\mathalpha}{mathematical italic nabla}%
\UnicodeMathSymbol{"1D735}{\mbfitnabla     }{\mathalpha}{mathematical bold italic nabla}%
\UnicodeMathSymbol{"1D76F}{\mbfsansnabla   }{\mathalpha}{mathematical sans-serif bold nabla}%
\UnicodeMathSymbol{"1D7A9}{\mbfitsansnabla }{\mathalpha}{mathematical sans-serif bold italic nabla}%

So, if you want to use bold variant of nabla, you can set

\let\nabla=\mbfnabla

That is all. More things are simpler with Unicode math.