version 1.7, 2000/01/15 06:11:17 |
version 1.10, 2000/01/16 10:58:19 |
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% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.6 2000/01/15 03:47:59 takayama Exp $ |
% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.9 2000/01/16 06:39:39 takayama Exp $ |
\section{Applications} |
\section{Applications} |
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\subsection{Heterogeneous Servers} |
\subsection{Heterogeneous Servers} |
Line 14 We can build a new computer math system by assembling |
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Line 14 We can build a new computer math system by assembling |
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different OpenXM servers. |
different OpenXM servers. |
It is similar to building a toy house by LEGO blocks. |
It is similar to building a toy house by LEGO blocks. |
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We will see two examples of custom made systems |
We will see two examples of custom-made systems |
built by OpenXM servers. |
built by OpenXM servers. |
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\subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir} |
\subsubsection{Computation of annihilating ideals by kan/sm1 and ox\_asir} |
Line 36 His algorithm reduces the problem to computations of G |
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Line 36 His algorithm reduces the problem to computations of G |
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in $D$ and to find the maximal integral root of a polynomial. |
in $D$ and to find the maximal 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 |
ox\_asir, to factorize polynomials to find the integral |
{\tt ox\_asir}, to factorize polynomials to find the integral |
roots. |
roots. |
These two OpenXM complient systems are integrated by |
These two OpenXM compliant systems are integrated by |
OpenXM protocol. |
the OpenXM protocol. |
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For example, the following is a sm1 session to find the annihilating |
For example, the following is a sm1 session to find the annihilating |
ideal for $f = x^3 - y^2 z^2$. |
ideal for $f = x^3 - y^2 z^2$. |
Line 63 an algorithm to stratify singularity |
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Line 63 an algorithm to stratify singularity |
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\cite{oaku-advance} |
\cite{oaku-advance} |
is implemented by |
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 |
ox\_asir, for primary ideal decompositions. |
{\tt ox\_asir}, for primary ideal decompositions. |
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\subsubsection{A Course on Solving Algebraic Equations} |
\subsubsection{A Course on Solving Algebraic Equations} |
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Risa/asir \cite{asir} is a general computer algebra system |
Risa/Asir \cite{asir} is a general computer algebra system |
which is good at Gr\"obner basis computations for zero dimensional ideal |
which can be used for Gr\"obner basis computations for zero dimensional ideal |
with ${\bf Q}$ coefficients. |
with ${\bf Q}$ coefficients. |
However, it is not good at graphical presentations and |
However, it is not good at graphical presentations and |
numerical methods. |
numerical methods. |
We integrated Risa/asir, ox\_phc (based on PHC pack by Verschelde \cite{phc} |
We integrated Risa/Asir, ox\_phc (based on PHC pack by Verschelde \cite{phc} |
for the polyhedral homotopy method) and |
for the polyhedral homotopy method) and |
ox\_gnuplot (GNUPLOT) servers |
ox\_gnuplot (GNUPLOT) servers |
to teach a course on solving algebraic equations. |
to teach a course on solving algebraic equations. |
This course was presented with the text book \cite{CLO} which discusses |
This course was presented with the text book \cite{CLO}, |
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which discusses |
on the Gr\"obner basis method and the polyhedral homotopy method |
on the Gr\"obner basis method and the polyhedral homotopy method |
to solve systems of algebraic equations. |
to solve systems of algebraic equations. |
We could teach a 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 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. |
the PHC pack (Figure \ref{katsura} is the output of {\tt [292]}): |
\begin{verbatim} |
\begin{verbatim} |
[287] phc(katsura(7)); |
[287] phc(katsura(7)); |
The detailed output is in the file tmp.output.* |
The detailed output is in the file tmp.output.* |