version 1.10, 2000/01/16 10:58:19 |
version 1.13, 2000/01/17 08:50:56 |
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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 1.12 2000/01/17 08:06:15 noro Exp $ |
\section{Applications} |
\section{Applications} |
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\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 $f^{-1}$. |
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Line 33 equations for the function $f^{-1}$. |
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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 |
Line 82 on the Gr\"obner basis method and the polyhedral homot |
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Line 82 on the Gr\"obner basis method and the polyhedral homot |
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to solve systems of algebraic equations. |
to solve systems of algebraic equations. |
We taught the course |
We taught the course |
with a unified environment |
with a unified environment |
controlled by Asir user language, which is similar to C. |
controlled by the Asir user language, which is similar to C. |
The following is an Asir session to solve algebraic equations by calling |
The following is an Asir session to solve algebraic equations by calling |
the PHC pack (Figure \ref{katsura} is the output of {\tt [292]}): |
the PHC pack (Figure \ref{katsura} is the output of {\tt [292]}): |
\begin{verbatim} |
\begin{verbatim} |