! Argument of \@Aboxed has an extra }

Question

I have a problem using \Aboxed in the following align*-environment:

\begin{align*}
\omega(\sigma_{ij}) &\equiv 1 - \left(\frac{27J_3}{2\sigma_e^3}\right)^2 \\
& = \omega(L) = 1 - \frac{\left( 9L - L^3\right)^2}{\left(L^2+3\right)^3}. 
\end{align*}

I want to use \Aboxed to put the last part of the final equation in a box, i.e.

\begin{align*}
\omega(\sigma_{ij}) &\equiv 1 - \left(\frac{27J_3}{2\sigma_e^3}\right)^2 \\
& = \Aboxed{ \omega(L) = 1 - \frac{\left( 9L - L^3\right)^2}{\left(L^2+3\right)^3}. }
\end{align*}

This gives me the error message in the title. However, using \Aboxed in the upper equation of the align* doesn't cause any problems at all. I've also used \Aboxed in the last equation of other align*'s and align's in my document. What causes the error in this case?

Answer 1

\Aboxed (From mathtools) is designed to put a box across an alignment point (Refer mathtools documentation, section- 3.4.5, page 18). Hence,

\Aboxed{\omega(\sigma_{ij}) &\equiv 1 - \left(\frac{27J_3}{2\sigma_e^3}\right)^2 }\

works. The \Aboxed command is defined as (from mathtools.sty)

\newcommand\Aboxed[1]{\@Aboxed#1\ENDDNE}
\def\@Aboxed#1&#2\ENDDNE{%
  \settowidth\@tempdima{$\displaystyle#1{}$}%
  \addtolength\@tempdima{\fboxsep}%
  \addtolength\@tempdima{\fboxrule}%
  \global\@tempdima=\@tempdima
  \kern\@tempdima
  &
  \kern-\@tempdima
  \boxed{#1#2}
}

Hence, when you use \Aboxed, TeX will greedily look for an & (alignment character) and when it is not found, an error is returned.

If you want a box only for a portion without an alignment point inside, you can use boxed (basically from amsmath and mathtools loads amsmath also) as

& = \boxed{ \omega(L) = 1 - \frac{\left( 9L - L^3\right)^2}{\left(L^2+3\right)^3}. }

The boxed command is defined as (from amsmath.sty)

\newcommand{\boxed}[1]{\fbox{\m@th$\displaystyle#1$}}

which does not have any concern for the alignment character &. (Hence it will not work across &.)

Conclusion: If you want a box to cross through an alignment point, use \Aboxed. On the other hand, if the box is for only a portion without alignment point, use \boxed

Complete MWE will be:

\documentclass{article}
\usepackage{mathtools}
\begin{document}

\begin{align*}
\Aboxed{\omega(\sigma_{ij}) &\equiv 1 - \left(\frac{27J_3}{2\sigma_e^3}\right)^2 }\\
& = \boxed{ \omega(L) = 1 - \frac{\left( 9L - L^3\right)^2}{\left(L^2+3\right)^3}. }
\end{align*}


\end{document}