\section{MuPAD}

Here, we present some basic features of MuPAD and its MuPACS
interface.

\section{Standard computer algebra stuff}

\begin{Mexin}
  1+1
\end{Mexin}

\begin{Mexin}
  factor(1-x^10)
\end{Mexin}

\newpage
\section{Long names, libraries, automatic completion}
\begin{Mexin}
  combinat::partitions::list(10);
\end{Mexin}
\begin{Mexin}
  alias(part=combinat::partitions):
  part::count(4);
  part::list(4);
  map(part::list(4), part::printPretty);
\end{Mexin}

\newpage
\section{Typing (domains)}
\begin{Mexin}
  P2 := Dom::UnivariatePolynomial(x, Dom::IntegerMod(2)):
  p  := P2(x+1);
  domtype(p);
  p^2
\end{Mexin}
\begin{Mexin}
Q := Dom::Rational:
Qx := Dom::Fraction(Dom::DistributedPolynomial([x], Q)):
F := Dom::AlgebraicExtension(Qx, poly(z^2 - x, [z])):
P := Dom::DistributedPolynomial([u], F):
\end{Mexin}
  \begin{Mexin}
P(u*z)*P(z)
  \end{Mexin}
  \begin{Mexout}
                              x u
  \end{Mexout}
  \begin{Mexin}
factor(P(u^2 - x^3))
  \end{Mexin}
  \begin{Mexout}
                      (u + x z) (u - x z)
  \end{Mexout}
