Widehat with right arrow

Question

I am searching for a wide hat with a right arrow. So far I've found only the regular wide hat (\widehat, shown at the left of the image), or a curved right arrow (\curvearrowright).

Is there a way to get something like what I have badly drawn at the right of the image?

Answer 1

I provide two TikZ solutions.

1. The first one uses uses an empty node before and after the formula that belongs under the wide hat.
   • Disadvantage: The added vertical height will not be taken into calculation
   • Advantage: Math style (display, text, script, scriptscript) is not effected (other then in the \vphantom.
2. The second one is a node.
   • Disadvantage: Math style is lost. (Change the first \frac into a \tfrac to realize.)
   • Advantage: Vertical height is known to math mode.

Another disadvantage over \widehat is, that the line width doesn't change over the course of the path.

MWE

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{calc,arrows}

% Solution 1
\newcounter{tikzmark}
\newcommand{\tikzmark}[2][]{\tikz[baseline, inner sep=0, overlay, remember picture] \node[anchor=base] (#2) {\vphantom{#1}};}

\newcommand{\widehatarrow}[1]{%
    \tikzmark[#1]{widehatarrow\thetikzmark} #1 \tikzmark[#1]{endwidehatarrow\thetikzmark}%
    \tikz[overlay, remember picture] \draw[-to] (widehatarrow\thetikzmark.north)++(.05em,.4ex) -- ($(widehatarrow\thetikzmark.north)!.5!(endwidehatarrow\thetikzmark.north)+(.05em,.8ex)$) -- ($(endwidehatarrow\thetikzmark.north)+(.05em,.4ex)$);%
    \stepcounter{tikzmark}%
}

% Solution 2
\newcommand{\Widehatarrow}[1]{%
\tikz[baseline] {
    \node[inner sep=0, anchor=base] (widehatarrow){$#1$};
    \draw[-to] (widehatarrow.north west)++(.05em,.4ex) -- ($(widehatarrow.north west)!.5!(widehatarrow.north east)+(.05em,.8ex)$) -- ($(widehatarrow.north east)+(.05em,.4ex)$);%
    }%
}


\begin{document}
\begin{equation} % Solution 1
\widehatarrow{A, B} \cdot \widehatarrow{x, y} = \widehatarrow{A, y, B, x}
\end{equation}

\begin{equation} % Solution 2
\Widehatarrow{A, B} \cdot \Widehatarrow{x, y} = \Widehatarrow{A, y, B, x}
\end{equation}

\begin{equation} % Compare both solutions
 \frac{1}{\widehatarrow{A, B} \cdot \Widehatarrow{A, B}} = \frac{1}{\widehatarrow{A, B} \cdot \widehatarrow{A, B}} = \frac{1}{\Widehatarrow{A, B} \cdot \Widehatarrow{A, B}}
\end{equation}
\end{document}

Output

---

(By egreg) It's possible to overcome the limitations with \Widehatarrow, by using a \vphantom and \mathpalette:

\newcommand{\Widehatarrow}[1]{\mathpalette\Widehatarrowaux{#1}}
\newcommand{\Widehatarrowaux}[2]{%
  \vphantom{#1\widehat{#2}}
  \tikz[baseline] {
    \node[inner sep=0, anchor=base] (widehatarrow){$#1#2$};
    \draw[-to] (widehatarrow.north west)++(.05em,.4ex)
     -- ($(widehatarrow.north west)!.5!(widehatarrow.north east)+(.05em,.8ex)$)
     -- ($(widehatarrow.north east)+(.05em,.4ex)$);%
  }%
}

Now the height of \Widehatarrow{AB} will be the same as the height of \widehat{AB} and the sizes will be respected, as shown by trying

$\Widehatarrow{AB}=A_{\Widehatarrow{XY}}$