Wie schreibe ich ttfamily im Mathemodus (und im Textmodus)?

\documentclass[]{article}

\usepackage{xparse}
\usepackage{amssymb}

\renewcommand*\familydefault{\ttdefault}
\usepackage{mathastext}
\renewcommand*\familydefault{\rmdefault}

\makeatletter
\newsavebox\ttrulebox
\newcommand\ttrule[2][0pt]
  {%
    \raisebox{#1}
      {%
        \begingroup
        \setbox\ttrulebox\hbox{\_}%
        \count0=\numexpr#2/\wd\ttrulebox\relax
        \ifdim#2>\count0\wd\ttrulebox
          \advance\count0by1
        \fi
        \leaders\hbox{\_}\hskip\count0\wd\ttrulebox
        \endgroup
      }%
  }
\NewDocumentCommand\ttsqrt{om}
  {%
    \IfValueTF{#1}
      {\sqrt[{#1}]}%
      {\sqrt}%
      {\vphantom{#2}}%
    \mathpalette\ttsqrt@{#2}%
  }
\newcommand\ttsqrt@[2]
  {%
    \setbox0\hbox{$#1#2$}%
    \rlap{\ttrule[\dimexpr\ht0+2pt]{\wd0}}%
    #2%
  }
\newcommand\ttfrac[2]
  {%
    \mathpalette\ttfrac@a{{#1}{#2}}%
  }
\newcommand\ttfrac@a[2]
  {%
    \ttfrac@b#1#2%
  }
\newcommand\ttfrac@b[3]
  {%
    \begingroup
    \setbox0\hbox{$#1#2$}%
    \setbox2\hbox{$#1#3$}%
    \dimen0=\ifdim\wd0>\wd2\wd0\else\wd2\fi
    \setbox4\hbox{\ttrule{\dimen0}}%
    \dimen0=\ifdim\dimen0>\wd4\dimen0\else\wd4\fi
    \raise.5ex\hbox
      {%
        \rlap{\raise\dimexpr\dp0+2pt\hbox to \dimen0{\hss\box0\hss}}%
        \rlap{\box4}%
        \lower\dimexpr\ht2+2pt\hbox to \dimen0{\hss\box2\hss}%
      }%
    \endgroup
  }
\NewDocumentCommand\ttint{e{^_}}
  {%
    \mathchoice
      {\ttint@\displaystyle\scriptstyle{#1}{#2}}%
      {\ttint@\textstyle\scriptstyle{#1}{#2}}%
      {\ttint@\scriptstyle\scriptscriptstyle{#1}{#2}}%
      {\ttint@\scriptscriptstyle\scriptscriptstyle{#1}{#2}}%
  }
\newcommand\ttint@symbol[1]
  {%
    \begingroup
    \setbox0\hbox{$#1\texttt{|}$}%
    \rlap{$#1\mkern3.5mu\raise0.4\ht0\hbox{$#1\texttt{\string^}$}$}%
    \rlap{$#1\mkern1.9mu\texttt{|}$}%
    \rlap{$#1\lower\dimexpr\dp0+1.5ex\relax\hbox{$#1\texttt{ˇ}$}$}%
    \mkern12mu
    \endgroup
  }
\newcommand\ttint@[4]
  {%
    \begingroup
    \mkern3mu
    \setbox0\hbox{$#1\ttint@symbol{#1}$}%
    \setbox2\hbox{\IfValueT{#3}{$#2#3$}}%
    \setbox4\hbox{\IfValueT{#4}{$#2#4$}}%
    \dimen0=\ifdim\wd0>\wd2\wd0\else\wd2\fi
    \dimen0=\ifdim\dimen0>\wd4\dimen0\else\wd4\fi
    \rlap{\raise\dimexpr\ht0+\dp2+2pt\hbox to \dimen0{\hss\box2\hss}}%
    \rlap{\lower\dimexpr.3\dp0+\ht4+2pt\hbox to \dimen0{\hss\box4\hss}}%
    \hbox to \dimen0{\hss\box0\hss}%
    \endgroup
  }
\makeatother

\begin{document}
Dies ist Text, aber Einstein hat herausgefunden, dass
\begin{equation}
  E=mc^2
\end{equation}
gilt. Außerdem gibt es Wurzeln und Brüche in der Mathematik
\begin{equation}
  \ttsqrt{4} = \ttfrac{\ttfrac{8}{2}}{2} = \ttsqrt[3]{\ttfrac{16}{2}}
\end{equation}
Eine einfache Stammfunktion lautet
\begin{equation}
  \ttint x\,dx = \ttfrac{1}{2}x^2 + c
\end{equation}
während das bestimmte Integral ausgewertet werden kann
\begin{equation}
  \ttint_0^2 4\,dx = 8
\end{equation}
\end{document}

% arara: lualatex
\documentclass{article}
\usepackage{typewriter}
\usepackage{blindtext}
\begin{document}

\blindmathpaper

\end{document}