=================================================================== RCS file: /home/cvs/OpenXM/doc/issac2000/heterotic-network.tex,v retrieving revision 1.9 retrieving revision 1.10 diff -u -p -r1.9 -r1.10 --- OpenXM/doc/issac2000/heterotic-network.tex 2000/01/16 06:39:39 1.9 +++ OpenXM/doc/issac2000/heterotic-network.tex 2000/01/16 10:58:19 1.10 @@ -1,4 +1,4 @@ -% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.8 2000/01/15 06:26:06 takayama Exp $ +% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.9 2000/01/16 06:39:39 takayama Exp $ \section{Applications} \subsection{Heterogeneous Servers} @@ -14,7 +14,7 @@ We can build a new computer math system by assembling different OpenXM servers. It is similar to building a toy house by LEGO blocks. -We will see two examples of custom made systems +We will see two examples of custom-made systems built by OpenXM servers. \subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir} @@ -38,8 +38,8 @@ This algorithm (the function {\tt annfs}) is implement kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and {\tt ox\_asir}, to factorize polynomials to find the integral roots. -These two OpenXM complient systems are integrated by -OpenXM protocol. +These two OpenXM compliant systems are integrated by +the OpenXM protocol. For example, the following is a sm1 session to find the annihilating ideal for $f = x^3 - y^2 z^2$. @@ -80,7 +80,7 @@ This course was presented with the text book \cite{CLO which discusses on the Gr\"obner basis method and the polyhedral homotopy method to solve systems of algebraic equations. -We could teach a course +We taught the course with a unified environment controlled by Asir user language, which is similar to C. The following is an Asir session to solve algebraic equations by calling