Highlight equations by temporary changing the formatting of their number

Question

I am writing a long paper having 100+ equations, and want to highlight a few key equations. Since the journal won't let me use boxes around equations, I am trying to have their label being typeset differently, e.g. as (5*) instead of (5). This should only affect specific equations. I have been trying to set up a new environment similar to subequations, but without success.

Answer 1

I finally got what I wanted by (temporarily) redefining the parentheses around the equation numbers to include a star. This also works in other environments such as align

\documentclass{article}
\usepackage{amsmath}
\makeatletter
\newenvironment{highlightequation}{%
  \def\tagform@##1{\maketag@@@{(\ignorespaces##1\unskip\@@italiccorr*)}}%
  \ignorespaces
}{%
  \def\tagform@##1{\maketag@@@{(\ignorespaces##1\unskip\@@italiccorr)}}%
  \ignorespacesafterend
}
\makeatother    

\begin{document}
A highlighted equation:
\begin{highlightequation}
\begin{equation}
    t(s) = r'(s)
\end{equation}
\end{highlightequation}
A minor equation, needs no highlight:
\begin{equation}
    a(s) = b'(s)
\end{equation}
Highlighting also works amsmath environments, such as align:
\begin{highlightequation}
\begin{subequations}
\begin{align}
    t(s) & = r'(s) \\
    t(s) & = r'(s)
\end{align}
\end{highlightequation}
\end{subequations}
\end{document}

The result looks like this:

Answer 2

You can redefine the equation number printing mechanism \theequation to add the star * using a form of "switching":

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand{\eqspecialnum}{% Special equation numbering
  \renewcommand{\theequation}{\arabic{equation}*}}
\newcommand{\eqnormalnum}{% Regular equation numbering
  \renewcommand{\theequation}{\arabic{equation}}}
\begin{document}
Some text.
\begin{equation} f(x)=ax^2+bx+c \label{eqn:1}\end{equation}
Some more text. See \eqref{eqn:3}.
\begin{equation} f(x)=ax^2+bx+c \label{eqn:2}\end{equation}
And then some more text. \eqspecialnum % Switch to special numbering.
\begin{equation} f(x)=ax^2+bx+c \label{eqn:3}\end{equation}
And here is even more text.
\begin{equation} f(x)=ax^2+bx+c \label{eqn:4}\end{equation}
This piece of text is even longer. \eqnormalnum % Switch back to normal.
\begin{equation} f(x)=ax^2+bx+c \label{eqn:5}\end{equation}
The end.
\end{document}

Here \eqspecialnum switches the numbering scheme to have a star * appended to the equation number, while \eqnormalnum returns the default behaviour of the numbering. Referencing accommodates this redefinition, as can be seen in the given example.

Answer 3

This is a improved and combines solution of the already existing answers.

Werner’s answer can easily modified to make the new \theequation dependent on the old own by using its definition in

\expandafter\def\expandafter\theequation\expandafter{\theequation*}

Though it would be doable to strip the * in another redefinition of \theequation it is easier to just use the original definition that is stored with \let.

I also have added local variants \stareq and \nostareq that add or remove the * respectively.

Another solution, more along the lines of the OP’s answer is to used mathtools’ \newtagform and the switch \usetagform (internally it does basically the same with \maketag@@@ but provides a nicer interface). These tagform-changing solutions have the disadvantage of having to repeat ( and ) (which may be changed according to a different style).
The \stareq variant will still work, the \nostareq unfortunately won’t.

Code

\documentclass{article}
\usepackage{mathtools}
\let\origTheequation\theequation                                       % Solution 1
\newtagform{starred}{(}{*)}                                            % Solution 2

\newcommand{\eqspecialnum}{% Switch to starred version
    \let\origTheequation\theequation                                   % Solution 1
    \expandafter\def\expandafter\theequation\expandafter{\theequation*}% Solution 1
%   \usetagform{starred}%                                                Solution 2
}
\newcommand{\eqnormalnum}{% Switch to normal version
    \let\theequation\origTheequation                                   % Solution 1
%   \usetagform{default}%                                                Solution 2
}
\newcommand*{\stareq}{\stepcounter{equation}\tag{\theequation*}}       % Solution 1 and 2
\newcommand*{\nostareq}{\stepcounter{equation}\tag{\origTheequation}}  % Solution 1 only
\begin{document}
\begin{equation} f(x)=ax^2+bx+c \end{equation}
See \eqref{eqn:3} and \eqref{eqn:4}.
\begin{equation} f(x)=ax^2+bx+c \end{equation}
Switch to special numbering: \eqspecialnum % Switch to special numbering.
\begin{align} 
    f(x) & =ax^2+bx+c \label{eqn:3} \\
    f(x) & =ax^2+bx+c \label{eqn:4}
\end{align}
\begin{equation} f(x)=ax^2+bx+c \end{equation}
Switch back to normal:       \eqnormalnum 
\begin{equation} f(x)=ax^2+bx+c \end{equation}
\begin{equation} f(x)=ax^2+bx+c \stareq \end{equation}
\begin{equation} f(x)=ax^2+bx+c \end{equation}

Switch to special numbering: \eqspecialnum % Switch to special numbering.
\begin{align} 
    f(x) & =ax^2+bx+c \\
    f(x) & =ax^2+bx+c \nostareq
\end{align}
\begin{equation} f(x)=ax^2+bx+c \end{equation}
Switch back to normal:       \eqnormalnum 
\end{document}

Output