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% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.9 2000/01/16 06:39:39 takayama Exp $

% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.12 2000/01/17 08:06:15 noro Exp $

\section{Applications}

\subsection{Heterogeneous Servers}

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By using OpenXM, we can treat OpenXM servers essentially

like a subroutine.

Since OpenXM provides a universal stackmachine which does not

Since OpenXM provides a universal stack machine which does not

depend each servers,

it is relatively easy to install new servers.

We can build a new computer math system by assembling

Line 33 equations for the function $f^{-1}$.

An algorithm to determine generators of the annihilating ideal

was given by Oaku (see, e.g., \cite[5.3]{sst-book}).

His algorithm reduces the problem to computations of Gr\"obner bases

in $D$ and to find the maximal integral root of a polynomial.

in $D$ and to find the minimal integral root of a polynomial.

This algorithm (the function {\tt annfs}) is implemented by

kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and

{\tt ox\_asir}, to factorize polynomials to find the integral

Line 82 on the Gr\"obner basis method and the polyhedral homot

to solve systems of algebraic equations.

We taught the course

with a unified environment

controlled by Asir user language, which is similar to C.

controlled by the Asir user language, which is similar to C.

The following is an Asir session to solve algebraic equations by calling

the PHC pack (Figure \ref{katsura} is the output of {\tt [292]}):

\begin{verbatim}