===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/homogeneous-network.tex,v
retrieving revision 1.4
retrieving revision 1.7
diff -u -p -r1.4 -r1.7
--- OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/20 02:50:16	1.4
+++ OpenXM/doc/ascm2001p/homogeneous-network.tex	2001/06/20 05:42:47	1.7
@@ -1,31 +1,24 @@
-% $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.3 2001/06/20 02:39:25 noro Exp $
+% $OpenXM: OpenXM/doc/ascm2001p/homogeneous-network.tex,v 1.6 2001/06/20 03:18:21 noro 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. 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
-several types of distributed computation as follows.
+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
+%several types of distributed computation as follows.
 
 \subsubsection{Competitive distributed computation by various strategies}
 
 SINGULAR \cite{Singular} implements {\it 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 MP 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$
+extern Proc1,Proc2$ Proc1 = -1$ Proc2 = -1$
 /* G:set of polys; V:list of variables */
 /* Mod: the Ground field GF(Mod); O:type of order */
 def dgr(G,V,Mod,O)
@@ -49,9 +42,16 @@ 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}
 
+%%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.
@@ -133,7 +133,7 @@ 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 
@@ -151,7 +151,7 @@ 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));
@@ -250,7 +250,7 @@ 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