how to make fbox produce similar result to boxed from amsmath when used inside display math?

Question

I use Scientific word to generate Latex, and from its GUI, it only supports \fbox to put a frame around a displayed equation. i.e. I select the equation from the GUI and click on a button which adds a frame. The latex it generates adds fbox inside \[...\] and so I have no control over this.

What I can do is add something in the preamble of the latex file that can fix or improve something it does.

The problem is that \fbox seems to change the size of the math on the right side of the equation compared to the left side. When I do the same thing using \boxed I get much better result, which is what I want. (but again, the GUI generates \fbox and there is no way to tell SW to use boxed instead).

Here is a MWE and it is clear that fbox output is not right.

At first I thought if I make the fboxsep larger that will fix it, but that has no effect at all on the font size. Is there something else I can add to preamble to make the result look like \boxed?

One last thing, I can't just change \fbox by \boxed using some smart text replacement macro, as SW will not longer be able to display the equation on the screen then, since it does not know what \boxed is.

\documentclass[11pt]{article}%
\usepackage{amsmath}
\setlength{\fboxsep}{10pt}
\begin{document}

\[
\fbox{$x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}$}%
\]

\[
\boxed{x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}}%
\]

\end{document}

Result is

Answer 1

One way would be to explicitly switch to \displaystyle within \fbox. This way, the \[...\] can be omitted, unless it should be centered explicitly (well use \begin{center}...\end{center} or \centering (grouped!))

I added a command \mathfbox which does the \[...\] and the displaystyle automatically.

All three ways are shown in the screen shot. The \mathfbox output is the middle one!

\documentclass[11pt]{article}%
\usepackage{amsmath}
\setlength{\fboxsep}{10pt}

\newcommand{\mathfbox}[1]{%
  \[%
  \fbox{%
    \ensuremath{\displaystyle{#1}}%
  }% End of \fbox
  \]%
}%


\begin{document}

\[
\fbox{%
$\displaystyle x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)}}$}%
\]


\mathfbox{x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(1+t^2\right)}}}%

\[
\boxed{x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}}%
\]

\end{document}

This way both boxes look the same ... I suspect, that \boxed is doing nothing different than \fbox{\ensuremath{\displaystyle...}

Update, with redefined \fbox command

\documentclass[11pt]{article}%
\usepackage{amsmath}
\usepackage{xstring}
\usepackage{letltxmacro}% 
\setlength{\fboxsep}{10pt}
\begin{document}


\LetLtxMacro\LaTeXStandardFBox\fbox


\renewcommand{\fbox}[1]{%
  \LaTeXStandardFBox{%
    \expandarg
    \StrSubstitute[1]{#1}{$}{$\displaystyle}%
  }% End of \fbox
}%

\[
\fbox{$x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(1+t^2\right)}}$}%
\]

\let\fbox\LaTeXStandardFBox%
\[
\boxed{x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}}%
\]

\end{document}

Answer 2

As usual my advice is to drop front ends to LaTeX if they don't support basic constructions and, like SW, are based on older TeX distributions.

The solution I'll suggest is a hack that will possibly give bad results in other situations. Also, \boxed should be used very sparingly in general (“never” is a good approximation to “very sparingly”).

\documentclass[11pt]{article}
\usepackage{amsmath}

\let\latexfbox\fbox
\renewcommand{\fbox}[1]{%
  \latexfbox{\everymath{\displaystyle}#1}%
}

\begin{document}

\[
\fbox{$x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}$}%
\]

\[
\boxed{x_1\left(  t\right)  =x_{20}\frac{t}{1+t^2}+\frac{1}{\sqrt{\left(
1+t^2\right)  }}}%
\]

\end{document}