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version 1.2, 2001/09/23 08:31:18 version 1.3, 2001/09/25 01:17:08
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 %% $OpenXM: OpenXM/doc/ascm2001p/ohp.tex,v 1.1 2001/09/20 09:27:56 takayama Exp $  %% $OpenXM: OpenXM/doc/ascm2001p/ohp.tex,v 1.2 2001/09/23 08:31:18 takayama Exp $
 \documentclass{slides}  \documentclass{slides}
 %%\documentclass[12pt]{article}  %%\documentclass[12pt]{article}
 \usepackage{color}  \usepackage{color}
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 {\color{green} Design and Implementation of OpenXM-RFC 100 and 101}  {\color{green} Design and Implementation of OpenXM-RFC 100 and 101}
   
 \noindent  \noindent
 M.Maekawa, M.Noro, K.Ohara, N.Takayama, Y.Tamura \\  M.Maekawa ($BA0(B $B@n(B $B!!(B $B>-(B $B=((B), \\ M.Noro ($BLn(B $BO$(B $B!!(B $B@5(B $B9T(B), \\
 \htmladdnormallink{http://www.openxm.org}{http://www.openxm.org}  K.Ohara ($B>.(B $B86(B $B!!(B $B8y(B $BG$(B), \\ N.Takayama ($B9b(B $B;3(B $B!!(B $B?.(B $B5#(B), \\
   Y.Tamura ($BED(B $BB<(B $B!!(B $B63(B $B;N(B)\\
   \htmladdnormallink{{\color{red}http://www.openxm.org}}{{\color{red}http://www.openxm.org}}
   
   
 \newpage  \newpage
 \noindent  \noindent
 {\color{red} 1. Architecture} \\  {\color{red} 1. Architecture} \\
Line 21  Two main applications of the project \\
Line 24  Two main applications of the project \\
 \begin{enumerate}  \begin{enumerate}
 \item Providing an environment for interactive distributed computation.  \item Providing an environment for interactive distributed computation.
 {\color{blue} Risa/Asir}  {\color{blue} Risa/Asir}
   (computer algebra system for general purpose,
    open source (c) Fujitsu, \\
    http://www.openxm.org, \\
    http://risa.cs.ehime-u.ac.jp, \\
    http://www.math.kobe-u.ac.jp/Asir/asir.html)
 \item e-Bateman project  \item e-Bateman project
 (Electronic version of higher transcendental functions of the 21st century)\\  (Electronic version of higher transcendental functions of the 21st century)\\
 1st step: Generate and verify hypergeometric function identities.  1st step: Generate and verify hypergeometric function identities.
Line 131  ox_reset(P);
Line 139  ox_reset(P);
 \noindent{\color{red} 4. Easy to try and evaluate distributed algorithms} \\  \noindent{\color{red} 4. Easy to try and evaluate distributed algorithms} \\
   
 \noindent  \noindent
   {\color{green} Example 1} \\
 Theorem (Cantor-Zassenhaus) \\  Theorem (Cantor-Zassenhaus) \\
 Let $f_1$ and $f_2$ be degree $d$ polynomials in $F_q[x]$.  Let $f_1$ and $f_2$ be degree $d$ polynomials in $F_q[x]$.
 For a random degree $2d-1$ polynomial $g \in F_q[x]$,  For a random degree $2d-1$ polynomial $g \in F_q[x]$,
Line 195  def c_z(F,E,Level)
Line 204  def c_z(F,E,Level)
 }  }
 \end{verbatim}  \end{verbatim}
 \newpage  \newpage
   
   {\color{green} Example 2} \\
   Shoup's algorithm to multyply polynomials.
   \newpage
   
 \noindent  \noindent
 {\color{red} 5. e-Bateman project} \\  {\color{red} 5. e-Bateman project} \\
 First Step: \\  First Step: \\
Line 219  Erdelyi: {\color{green} Higher Transcendental Function
Line 233  Erdelyi: {\color{green} Higher Transcendental Function
 The solution space of the ordinary differential equation  The solution space of the ordinary differential equation
 $$ x(1-x) \frac{d^2f}{dx^2} -\left( c-(a+b+1)x \right) \frac{df}{dx} - a b f = 0$$  $$ x(1-x) \frac{d^2f}{dx^2} -\left( c-(a+b+1)x \right) \frac{df}{dx} - a b f = 0$$
 is spanned by  is spanned by
 $$ F(a,b,c;x) , \  x^{1-c} F(a,b,c;x) $$  $$ F(a,b,c;x) = {\color{red}1} + O(x), \
      x^{1-c} F(a,b,c;x) = {\color{red}x^{1-c}}+O(x^{2-c}))$$
   
 when $c \not\in {\bf Z}$. \\  when $c \not\in {\bf Z}$. \\
 {\color{blue} Formula (type B)}\\  {\color{blue} Formula (type B)}\\
 \begin{eqnarray*}  \begin{eqnarray*}
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