version 1.4, 2000/01/15 01:33:32 |
version 1.8, 2000/01/15 06:26:06 |
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% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.3 2000/01/03 04:27:52 takayama Exp $ |
% $OpenXM: OpenXM/doc/issac2000/heterotic-network.tex,v 1.7 2000/01/15 06:11:17 takayama Exp $ |
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\section{Applications} |
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\subsection{Heterogeneous Servers} |
\subsection{Heterogeneous Servers} |
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Line 13 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 special purpose 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 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 78 to teach a course on solving algebraic equations. |
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Line 79 to teach a course on solving algebraic equations. |
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This course was presented with the text book \cite{CLO} which discusses |
This course was presented with the text book \cite{CLO} 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. |
Risa/asir has a user language like C and we could teach a course |
We could teach a course |
with a unified environment |
with a unified environment |
controlled by asir user language. |
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 (see Figure \ref{katsura} too): |
\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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