\chapter{MODSR: Modular solve and roots}
\label{MODSR}
\typeout{{MODSR: Modular solve and roots}}
{\footnotesize
\begin{center}
Herbert Melenk \\
Konrad--Zuse--Zentrum f\"ur Informationstechnik Berlin \\
Takustra\"se 7 \\
D--14195 Berlin--Dahlem, Germany \\[0.05in]
e--mail: melenk@zib.de
\end{center}
}
\ttindex{MODSR}
This package supports solve (\f{M\_SOLVE}\ttindex{M\_SOLVE}) and roots
(\f{M\_ROOTS}\ttindex{M\_ROOTS}) operators for modular polynomials and
modular polynomial systems. The moduli need not be primes. {\tt
M\_SOLVE} requires a modulus to be set. {\tt M\_ROOTS} takes the
modulus as a second argument. For example:
\begin{verbatim}
on modular; setmod 8;
m_solve(2x=4); -> {{X=2},{X=6}}
m_solve({x^2-y^3=3});
-> {{X=0,Y=5}, {X=2,Y=1}, {X=4,Y=5}, {X=6,Y=1}}
m_solve({x=2,x^2-y^3=3}); -> {{X=2,Y=1}}
off modular;
m_roots(x^2-1,8); -> {1,3,5,7}
m_roots(x^3-x,7); -> {0,1,6}
\end{verbatim}