Override the spacing on the right of an in-line equation when followed by a punctuation mark

Question

I set \mathsurround to 2pt in order to have a bit more horizontal spacing between text and in-line equations. Is there a way to set it to 0pt on the right whenever the in-line equation is followed by a punctuation mark?

For instance, the code

Let $x=0$ and $y=1$.

is typeset as in the first line below, while I would like it to be as in the second.

Is there a way to achieve this without having to provide every time \hspace{-2pt}?

Edit:

I have already considered @barbarabeeton's advice, that is, to include the punctuation before the final $, but some marks are typeset differently in text mode and math mode. Probably punctuation marks is a bit too restrictive, as I would like to include brackets () [] {} or even the apostrophe '. In addition I would like my code to be flexible, so whenever I decide to change something I don't have to edit the whole document.

Answer 1

There are two ways. The first is to remove the math surround kern (with a macro before the punctuation); the second is to have punctuation inside the formula, but with a macro that takes care of the space factor and removes the kern.

In the example I show both methods. The third line is with zero `mathsurround, with the kerns added manually in order to show the output is the same.

\documentclass{article}

\newcommand{\unms}{\kern-\mathsurround}

\newcommand{\fp}[1]{%
  \mbox{#1}%
  \xdef\fpuncsf{%
    \kern-\mathsurround
    \spacefactor\the\sfcode`#1\relax
  }%
  \aftergroup\fpuncsf
}

\setlength{\mathsurround}{2pt}

\begin{document}

Let $x=0$ and $y=1$\unms. There was a sentence ending period.

Let $x=0$ and $y=1\fp.$ There was a sentence ending period.

%% check
\mathsurround=0pt\def\?{\kern2pt }

Let \?$x=0$\? and \?$y=1$. There was a sentence ending period.

\end{document}