===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/homogeneous-network.tex,v
retrieving revision 1.5
retrieving revision 1.8
diff -u -p -r1.5 -r1.8
--- OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/20 03:08:05	1.5
+++ OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/21 03:09:46	1.8
@@ -1,10 +1,10 @@
-% $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.4 2001/06/20 02:50:16 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}
 \label{section:homog}
 
 One of the aims of OpenXM is a parallel speedup by a distributed computation
-with homogeneous servers. 
+with homogeneous servers.  Let us see some examples.
 %As the current specification of OpenXM does
 %not include communication between servers, one cannot expect
 %the maximal parallel speedup. However it is possible to execute
@@ -12,18 +12,11 @@ with homogeneous servers. 
 
 \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
-illustrated as an example of distributed computation.
-Such a distributed computation is also possible on OpenXM as follows:
+illustrated as an example of distributed computation by the interface.
+Such a distributed computation is also possible on OpenXM.
 
-The client creates two servers and it requests 
-Gr\"obner basis comutations by the Buchberger algorithm the $F_4$ algorithm
-to the servers for the same input.
-The client watches the streams by {\tt ox\_select()}
-and the result which is returned first is taken. Then the remaining
-server is reset.
-
 \begin{verbatim}
 extern Proc1,Proc2$
 Proc1 = -1$ Proc2 = -1$
@@ -50,12 +43,15 @@ def dgr(G,V,Mod,O)
   return [Win,R];
 }
 \end{verbatim}
+In the above Asir program, the client creates two servers and it requests 
+Gr\"obner basis computations by the Buchberger algorithm 
+and the $F_4$ algorithm to the servers for the same input.
+The client watches the streams by {\tt ox\_select()}
+and the result which is returned first is taken. Then the remaining
+server is reset.
 
 \subsubsection{Nesting of client-server communication}
 
-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}
 \label{tree}
 \begin{center}
@@ -78,6 +74,12 @@ client-server communication.
 \caption{Tree-like structure of client-server communication}
 \end{center}
 \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
 algorithms whose task can be divided into subtasks recursively.  
 
@@ -134,13 +136,13 @@ algorithms whose task can be divided into subtasks rec
 %\end{verbatim}
 %
 A typical example is a parallelization of the Cantor-Zassenhaus
-algorithm for polynomial factorization over finite fields.
+algorithm for polynomial factorization over finite fields,
 which is a recursive algorithm.
 At each level of the recursion, a given polynomial can be
 divided into two non-trivial factors with some probability by using 
 a randomly generated polynomial as a {\it separator}.
 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
 itself. 
 %\begin{verbatim}
@@ -152,7 +154,7 @@ itself. 
 %  if ( N == E ) return [F];
 %  M = field_order_ff(); K = idiv(N,E); L = [F];
 %  while ( 1 ) {
-%    /* gererate a random polynomial */
+%    /* generate a random polynomial */
 %    W = monic_randpoly_ff(2*E,V);
 %    /* compute a power of the random polynomial */
 %    T = generic_pwrmod_ff(W,F,idiv(M^E-1,2));
@@ -251,7 +253,7 @@ work well on OpenXM.
 %Such a distributed computation is also possible on OpenXM as follows:
 %
 %The client creates two servers and it requests 
-%Gr\"obner basis comutations from the homogenized input and the input itself
+%Gr\"obner basis computations from the homogenized input and the input itself
 %to the servers.
 %The client watches the streams by {\tt ox\_select()}
 %and the result which is returned first is taken. Then the remaining