version 1.5, 2000/01/15 03:23:59 |
version 1.9, 2000/01/16 06:39:39 |
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% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.4 2000/01/15 01:33:32 takayama Exp $ |
% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.8 2000/01/15 06:26:06 takayama Exp $ |
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\section{Applications} |
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\subsection{Heterogeneous Servers} |
\subsection{Heterogeneous Servers} |
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Line 35 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 complient systems are integrated by |
OpenXM protocol. |
OpenXM protocol. |
Line 48 Starting ox_asir server. |
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Line 49 Starting ox_asir server. |
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Byte order for control process is network byte order. |
Byte order for control process is network byte order. |
Byte order for engine process is network byte order. |
Byte order for engine process is network byte order. |
[[-y*Dy+z*Dz, 2*x*Dx+3*y*Dy+6, -2*y*z^2*Dx-3*x^2*Dy, |
[[-y*Dy+z*Dz, 2*x*Dx+3*y*Dy+6, -2*y*z^2*Dx-3*x^2*Dy, |
-2*y^2*z*Dx-3*x^2*Dz, -2*z^3*Dx*Dz-3*x^2*Dy^2-2*z^2*Dx], |
-2*y^2*z*Dx-3*x^2*Dz, -2*z^3*Dx*Dz-3*x^2*Dy^2-2*z^2*Dx], |
[-1,-139968*s^7-1119744*s^6-3802464*s^5-7107264*s^4 |
[-1,-139968*s^7-1119744*s^6-3802464*s^5-7107264*s^4 |
-7898796*s^3-5220720*s^2-1900500*s-294000]] |
-7898796*s^3-5220720*s^2-1900500*s-294000]] |
\end{verbatim} |
\end{verbatim} |
Line 62 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 could teach a 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} |
[257] phc([x^2+y^2-4,x*y-1]); |
[287] phc(katsura(7)); |
The detailed output is in the file tmp.output.* |
The detailed output is in the file tmp.output.* |
The answer is in the variable Phc. |
The answer is in the variable Phc. |
0 |
0 |
[260] Phc ; |
[290] B=map(first,Phc)$ |
[[[-0.517638,0],[-1.93185,0]], |
[291] gnuplot_plotDots([],0)$ |
[[1.93185,0],[0.517638,0]], |
[292] gnuplot_plotDots(B,0)$ |
[[-1.93185,0],[-0.517638,0]], |
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[[0.517638,0],[1.93185,0]]] |
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[261] |
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\end{verbatim} |
\end{verbatim} |
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\begin{figure}[htbp] |
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\epsfxsize=8.5cm |
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\epsffile{katsura7.ps} |
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\caption{The first components of the solutions to the system of algebraic equations Katsura 7.} |
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\label{katsura} |
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\end{figure} |
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