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version 1.7, 2001/06/20 05:42:47 version 1.8, 2001/06/21 03:09:46
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 % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.6 2001/06/20 03:18:21 noro Exp $  % $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.7 2001/06/20 05:42:47 takayama Exp $
   
 \subsection{Distributed computation with homogeneous servers}  \subsection{Distributed computation with homogeneous servers}
 \label{section:homog}  \label{section:homog}
Line 12  with homogeneous servers.  Let us see some examples.
Line 12  with homogeneous servers.  Let us see some examples.
   
 \subsubsection{Competitive distributed computation by various strategies}  \subsubsection{Competitive distributed computation by various strategies}
   
 SINGULAR \cite{Singular} implements {\it MP} interface for distributed  SINGULAR \cite{Singular} implements MP interface for distributed
 computation and a competitive Gr\"obner basis computation is  computation and a competitive Gr\"obner basis computation is
 illustrated as an example of distributed computation by the MP interface.  illustrated as an example of distributed computation by the interface.
 Such a distributed computation is also possible on OpenXM.  Such a distributed computation is also possible on OpenXM.
   
 \begin{verbatim}  \begin{verbatim}
 extern Proc1,Proc2$ Proc1 = -1$ Proc2 = -1$  extern Proc1,Proc2$
   Proc1 = -1$ Proc2 = -1$
 /* G:set of polys; V:list of variables */  /* G:set of polys; V:list of variables */
 /* Mod: the Ground field GF(Mod); O:type of order */  /* Mod: the Ground field GF(Mod); O:type of order */
 def dgr(G,V,Mod,O)  def dgr(G,V,Mod,O)
Line 51  server is reset.
Line 52  server is reset.
   
 \subsubsection{Nesting of client-server communication}  \subsubsection{Nesting of client-server communication}
   
 %%Prog:  load ("dfff"); df_demo();  enter 100.  
 Under OpenXM-RFC 100 an OpenXM server can be a client of other servers.  
 Figure \ref{tree} illustrates a tree-like structure of an OpenXM  
 client-server communication.  
 \begin{figure}  \begin{figure}
 \label{tree}  \label{tree}
 \begin{center}  \begin{center}
Line 77  client-server communication.
Line 74  client-server communication.
 \caption{Tree-like structure of client-server communication}  \caption{Tree-like structure of client-server communication}
 \end{center}  \end{center}
 \end{figure}  \end{figure}
   %%Prog:  load ("dfff"); df_demo();  enter 100.
   Under OpenXM-RFC 100 an OpenXM server can be a client of other servers.
   %Figure \ref{tree}
   Figure 2
   illustrates a tree-like structure of an OpenXM
   client-server communication.
 Such a computational model is useful for parallel implementation of  Such a computational model is useful for parallel implementation of
 algorithms whose task can be divided into subtasks recursively.  algorithms whose task can be divided into subtasks recursively.
   
Line 139  At each level of the recursion, a given polynomial can
Line 142  At each level of the recursion, a given polynomial can
 divided into two non-trivial factors with some probability by using  divided into two non-trivial factors with some probability by using
 a randomly generated polynomial as a {\it separator}.  a randomly generated polynomial as a {\it separator}.
 We can apply the following simple parallelization:  We can apply the following simple parallelization:
 When two non-trivial factors are generated on a server,  when two non-trivial factors are generated on a server,
 one is sent to another server and the other factor is factorized on the server  one is sent to another server and the other factor is factorized on the server
 itself.  itself.
 %\begin{verbatim}  %\begin{verbatim}
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