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Diff for /OpenXM/doc/issac2000/heterotic-network.tex between version 1.10 and 1.12

version 1.10, 2000/01/16 10:58:19 version 1.12, 2000/01/17 08:06:15
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 % $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.9 2000/01/16 06:39:39 takayama Exp $  % $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.11 2000/01/17 07:06:53 noro Exp $
 \section{Applications}  \section{Applications}
   
 \subsection{Heterogeneous Servers}  \subsection{Heterogeneous Servers}
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 By using OpenXM, we can treat OpenXM servers essentially  By using OpenXM, we can treat OpenXM servers essentially
 like a subroutine.  like a subroutine.
 Since OpenXM provides a universal stackmachine which does not  Since OpenXM provides a universal stack machine which does not
 depend each servers,  depend each servers,
 it is relatively easy to install new servers.  it is relatively easy to install new servers.
 We can build a new computer math system by assembling  We can build a new computer math system by assembling
Line 33  equations for the function $f^{-1}$.
Line 33  equations for the function $f^{-1}$.
 An algorithm to determine generators of the annihilating ideal  An algorithm to determine generators of the annihilating ideal
 was given by Oaku (see, e.g., \cite[5.3]{sst-book}).  was given by Oaku (see, e.g., \cite[5.3]{sst-book}).
 His algorithm reduces the problem to computations of Gr\"obner bases  His algorithm reduces the problem to computations of Gr\"obner bases
 in $D$ and to find the maximal integral root of a polynomial.  in $D$ and to find the minimal integral root of a polynomial.
 This algorithm (the function {\tt annfs}) is implemented by  This algorithm (the function {\tt annfs}) is implemented by
 kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and  kan/sm1 \cite{kan}, for Gr\"obner basis computation in $D$, and
 {\tt ox\_asir}, to factorize polynomials to find the integral  {\tt ox\_asir}, to factorize polynomials to find the integral

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