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version 1.2, 2001/06/20 01:54:05 version 1.6, 2001/06/21 03:13:35
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 % $OpenXM: OpenXM/doc/ascm2001p/heterotic-network.tex,v 1.1 2001/06/19 07:32:58 noro Exp $  % $OpenXM: OpenXM/doc/ascm2001p/heterotic-network.tex,v 1.5 2001/06/21 00:15:34 takayama 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 stack machine which does not  Since OpenXM provides a universal stack machine which does not
 depend each servers,  depend on each server,
 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 mathematical software system by assembling
 different OpenXM servers.  different OpenXM servers.
 OpenXM servers currently provide 1077 functions  OpenXM servers currently provide 1077 functions
 \cite{openxm-1077}.  \cite{openxm-1077}.
 We can use these as building blocks for a new system.  We can use these as building blocks for a new system.
   
 We present an example of a custom-made system  %We present an example of a custom-made system
 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 104  built by OpenXM servers.
Line 104  built by OpenXM servers.
 %\label{katsura}  %\label{katsura}
 %\end{figure}  %\end{figure}
   
 \subsubsection{Asir-contrib-HG package to solve GKZ hypergeometric systems}  Asir-contrib/Hypergeometric package is an
   example of a custom-made system built by OpenXM servers.
 GKZ hypergeometric system is a system of linear partial differential  GKZ hypergeometric system is a system of linear partial differential
 equations associated to $A=(a_{ij})$  equations associated to $A=(a_{ij})$
 (an integer $d\times n$-matrix of rank $d$)  (an integer $d\times n$-matrix of rank $d$)
Line 113  and $\beta \in {\bf C}^d$.
Line 113  and $\beta \in {\bf C}^d$.
 The book by Saito, Sturmfels and Takayama \cite{sst-book}  The book by Saito, Sturmfels and Takayama \cite{sst-book}
 discusses algorithmic methods to construct series solutions of the GKZ  discusses algorithmic methods to construct series solutions of the GKZ
 system.  system.
 The current Asir-contrib-HG package is built in order to implement  The current Asir-contrib/Hypergeoemtric package is built in order to implement
 these algorithms.  these algorithms.
 What we need for the implementation are mainly  What we need for the implementation are mainly
 (1) Gr\"obner basis computation both in the ring of polynomials  (1) Gr\"obner basis computation both in the ring of polynomials
Line 125  Asir and kan/sm1 provide functions for (1),
Line 125  Asir and kan/sm1 provide functions for (1),
 {\tt TiGERS} provides a function for (2),  {\tt TiGERS} provides a function for (2),
 and  and
 Asir provides a function for (3).  Asir provides a function for (3).
 These software systems communicate each other by OpenXM-RFC 100 protocol  These software systems communicate with each other
   by the OpenXM-RFC 100 protocol
 and form a unified package for GKZ hypergeometric systems.  and form a unified package for GKZ hypergeometric systems.
 See the chapter of dsolv of Asir Contrib User's manual \cite{openxm-web}  See the chapter of {\tt dsolv} of Asir Contrib User's manual \cite{openxm-web}
   for details.
   
 %Let us see an example how to construct series solution of a GKZ hypergeometric  %Let us see an example how to construct series solution of a GKZ hypergeometric
 %system.  %system.
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