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version 1.9, 2000/01/16 06:39:39 version 1.12, 2000/01/17 08:06:15
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 % $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.8 2000/01/15 06:26:06 takayama Exp $  % $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.11 2000/01/17 07:06:53 noro Exp $
 \section{Applications}  \section{Applications}
   
 \subsection{Heterogeneous Servers}  \subsection{Heterogeneous Servers}
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 By using OpenXM, we can treat OpenXM servers essentially  By using OpenXM, we can treat OpenXM servers essentially
 like a subroutine.  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,  depend each servers,
 it is relatively easy to install new servers.  it is relatively easy to install new servers.
 We can build a new computer math system by assembling  We can build a new computer math system by assembling
 different OpenXM servers.  different OpenXM servers.
 It is similar to building a toy house by LEGO blocks.  It is similar to building a toy house by LEGO blocks.
   
 We will see two examples of custom made systems  We will see two examples of custom-made systems
 built by OpenXM servers.  built by OpenXM servers.
   
 \subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir}  \subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir}
Line 33  equations for the function $f^{-1}$.
Line 33  equations for the function $f^{-1}$.
 An algorithm to determine generators of the annihilating ideal  An algorithm to determine generators of the annihilating ideal
 was given by Oaku (see, e.g., \cite[5.3]{sst-book}).  was given by Oaku (see, e.g., \cite[5.3]{sst-book}).
 His algorithm reduces the problem to computations of Gr\"obner bases  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  This algorithm (the function {\tt annfs}) is implemented by
 kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and  kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and
 {\tt ox\_asir}, to factorize polynomials to find the integral  {\tt ox\_asir}, to factorize polynomials to find the integral
 roots.  roots.
 These two OpenXM complient systems are integrated by  These two OpenXM compliant systems are integrated by
 OpenXM protocol.  the OpenXM protocol.
   
 For example, the following is a sm1 session to find the annihilating  For example, the following is a sm1 session to find the annihilating
 ideal for $f = x^3 - y^2 z^2$.  ideal for $f = x^3 - y^2 z^2$.
Line 80  This course was presented with the text book \cite{CLO
Line 80  This course was presented with the text book \cite{CLO
 which discusses  which discusses
 on the Gr\"obner basis method and the polyhedral homotopy method  on the Gr\"obner basis method and the polyhedral homotopy method
 to solve systems of algebraic equations.  to solve systems of algebraic equations.
 We could teach a course  We taught the course
 with a unified environment  with a unified environment
 controlled by Asir user language, which is similar to C.  controlled by Asir user language, which is similar to C.
 The following is an Asir session to solve algebraic equations by calling  The following is an Asir session to solve algebraic equations by calling
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