===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/heterotic-network.tex,v
retrieving revision 1.2
retrieving revision 1.6
diff -u -p -r1.2 -r1.6
--- OpenXM/doc/ascm2001p/heterotic-network.tex	2001/06/20 01:54:05	1.2
+++ OpenXM/doc/ascm2001p/heterotic-network.tex	2001/06/21 03:13:35	1.6
@@ -1,4 +1,4 @@
-% $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}
 
 \subsection{Heterogeneous Servers}
@@ -8,16 +8,16 @@
 By using OpenXM, we can treat OpenXM servers essentially 
 like a subroutine.
 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.
-We can build a new computer math system by assembling
+We can build a new mathematical software system by assembling
 different OpenXM servers.
 OpenXM servers currently provide 1077 functions
 \cite{openxm-1077}.
 We can use these as building blocks for a new system.
 
-We present an example of a custom-made system
-built by OpenXM servers.
+%We present an example of a custom-made system
+%built by OpenXM servers.
 
 %\subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir}
 %
@@ -104,8 +104,8 @@ built by OpenXM servers.
 %\label{katsura}
 %\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
 equations associated to $A=(a_{ij})$  
 (an integer $d\times n$-matrix of rank $d$)
@@ -113,7 +113,7 @@ and $\beta \in {\bf C}^d$.
 The book by Saito, Sturmfels and Takayama \cite{sst-book}
 discusses algorithmic methods to construct series solutions of the GKZ
 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.
 What we need for the implementation are mainly
 (1) Gr\"obner basis computation both in the ring of polynomials
@@ -125,9 +125,11 @@ Asir and kan/sm1 provide functions for (1),
 {\tt TiGERS} provides a function for (2),
 and
 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.
-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
 %system.