How to change catcode in environment

Question

I try to locally change catcode in environment

\newenvironment{wse}
{
  \catcode`^=\active%
  \def^{\mathchar\numexpr"7000+`\^\relax}%
  $
}
{
  $
}

but the next code

\begin{wse}
  x^2
\end{wse}

breaks with

! Missing control sequence inserted.

What is wrong?

Answer 1

When you do \newenvironment, the category code of ^ is 7 and this is not changed by \catcode`^=\active.

\begingroup
\catcode`^=\active
\gdef\changehat{\def^{\mathchar\numexpr"7000+`\^\relax}}
\endgroup

\newenvironment{wse}
 {%
  \catcode`^=\active
  \changehat
  $%
 }
 {%
  $%
 }

Full example

\documentclass{article}

\begingroup
\catcode`^=\active
\gdef\changehat{\def^{\mathchar\numexpr"7000+`\^\relax}}
\endgroup

\newenvironment{wse}
 {%
  \catcode`^=\active
  \changehat
  $%
 }
 {%
  $%
 }

\begin{document}

X$a^b$X\begin{wse}a^b\end{wse}X

\end{document}

An alternative with the \lowercase trick that assumes ~ is active.

\documentclass{article}

\newenvironment{wse}
 {%
  \catcode`^=\active
  \begingroup\lccode`~=`\^ \lowercase{\endgroup
    \def~{\mathchar\numexpr"7000+`\^\relax}}%
  $%
 }
 {%
  $%
 }

\begin{document}

X$a^b$X\begin{wse}a^b\end{wse}X

\end{document}