version 1.9, 2000/01/16 06:39:39 |
version 1.10, 2000/01/16 10:58:19 |
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% $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} |
\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 38 This algorithm (the function {\tt annfs}) is implement |
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Line 38 This algorithm (the function {\tt annfs}) is implement |
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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 |
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 80 This course was presented with the text book \cite{CLO |
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Line 80 This course was presented with the text book \cite{CLO |
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which discusses |
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 |