===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/ohp.tex,v
retrieving revision 1.1
retrieving revision 1.5
diff -u -p -r1.1 -r1.5
--- OpenXM/doc/ascm2001p/ohp.tex	2001/09/20 09:27:56	1.1
+++ OpenXM/doc/ascm2001p/ohp.tex	2001/09/29 08:33:41	1.5
@@ -1,4 +1,4 @@
-%% $OpenXM$
+%% $OpenXM: OpenXM/doc/ascm2001p/ohp.tex,v 1.4 2001/09/25 02:28:27 takayama Exp $
 \documentclass{slides}
 %%\documentclass[12pt]{article}
 \usepackage{color}
@@ -9,9 +9,12 @@
 {\color{green} Design and Implementation of OpenXM-RFC 100 and 101}
 
 \noindent
-M.Maekawa, M.Noro, K.Ohara, N.Takayama, Y.Tamura \\
-\htmladdnormallink{http://www.openxm.org}{http://www.openxm.org}
+M.Maekawa (前 川 　 将 秀), \\ M.Noro (野 呂 　 正 行), \\
+K.Ohara (小 原 　 功 任), \\ N.Takayama (高 山 　 信 毅), \\
+Y.Tamura (田 村 　 恭 士)\\
+\htmladdnormallink{{\color{red}http://www.openxm.org}}{{\color{red}http://www.openxm.org}}
 
+
 \newpage
 \noindent
 {\color{red} 1. Architecture} \\
@@ -21,6 +24,11 @@ Two main applications of the project \\
 \begin{enumerate}
 \item Providing an environment for interactive distributed computation.
 {\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 
 (Electronic version of higher transcendental functions of the 21st century)\\
 1st step: Generate and verify hypergeometric function identities.
@@ -36,7 +44,7 @@ OpenXM-RFC 100 \\
 OpenXM {\color{red} stackmachine}.
 \item execute\_string
 \begin{verbatim}
-  P = ox_launch(0,"ox_asir");
+  Pid = ox_launch(0,"ox_asir");
   ox_execute_string(Pid," poly_factor(x^10-1);");
 \end{verbatim}
 \end{enumerate}
@@ -128,11 +136,75 @@ ox_reset(P);
 \end{picture}
 \newpage
 
-\noindent{\color{red} 4. Easy to try and evaluate distributed algorithms} \\
+\noindent
+{\color{red} 4. e-Bateman project} (Electronic mathematical formula book)\\
+First Step: \\
+Gauss Hypergeometric function:
+$$ {\color{blue} F(a,b,c;x)} = \sum_{n=1}^\infty
+  \frac{(a)_n (b)_n}{(1)_n (c)_n} x^n
+$$
+where
+$$ (a)_n = a(a+1) \cdots (a+n-1). $$
+{\color{green}
+$$ \log (1+x) = x F(1,1,2;-x) $$
+$$ \arcsin x = x F(1/2,1/2,3/2;x^2) $$
+}
 
 \noindent
+Appell's $F_1$:
+$$ {\color{blue} F_1(a,b,b',c;x,y)} = \sum_{m,n=1}^\infty
+  \frac{(a)_{m+n} (b)_m (b')_n}{(c)_{m+n}(1)_m (1)_n} x^m y^n.
+$$
+\newpage
+Mathematical formula book, e.g.,
+Erdelyi: {\color{green} Higher Transcendental Functions} \\
+{\color{blue} Formula (type A)}\\
+The solution space of the ordinary differential equation
+$$ x(1-x) \frac{d^2f}{dx^2} -\left( c-(a+b+1)x \right) \frac{df}{dx} - a b f = 0$$
+is spanned by
+$$ F(a,b,c;x) = {\color{red}1} + O(x), \  
+   x^{1-c} F(a,b,c;x) = {\color{red}x^{1-c}}+O(x^{2-c}))$$
+
+when $c \not\in {\bf Z}$. \\
+{\color{blue} Formula (type B)}\\
+\begin{eqnarray*}
+&\ & F(a_1, a_2, b_2;z) \, F(-a_1,-a_2,2-b_2;z)  \\
+&+& \frac{z}{e_2}\, F'(a_1, a_2, b_2;z) \, F(-a_1,-a_2,2-b_2;z)  \\
+&-& \frac{z}{e_2}\, F(a_1, a_2, b_2;z) \, F'(-a_1,-a_2,2-b_2;z)  \\
+&-& \frac{a_1+a_2-e_2}{a_1 a_2 e_2}z^2\,
+  F'(a_1, a_2, b_2;z)\,F'(-a_1,-a_2,2-b_2;z) \\
+&=& 1
+\end{eqnarray*}
+where $e_2 = b_2-1$ and $a_1, a_2, e_2, e_2-a_2 \not\in {\bf Z}$.  \\
+(generalization of $\sin^2 x + \cos^2 x =1$.)
+
+\noindent
+Project in progress: \\
+We are trying to generate or verify type A formulas and type B formulas
+for {\color{blue} GKZ hypergeometric systems}.
+
+\begin{tabular}{|c|c|c|}
+\hline
+  & type A & type B \\ \hline
+Algorithm &  {\color{red} OK} (SST book) &  in progress \\ \hline
+Implementation & partially done & NO \\ \hline
+\end{tabular}
+
+\noindent
+Our ox servers
+{\tt ox\_asir}, {\tt ox\_sm1}, {\tt ox\_tigers}, {\tt ox\_gnuplot},
+{\tt ox\_mathematica}, {\tt OpenMathproxy} (JavaClasses), {\tt ox\_m2}
+are used to generate, verify and present formulas of type A
+for GKZ hypergeometric systems.
+
+\newpage
+
+\noindent{\color{red} 5. Easy to try and evaluate distributed algorithms} \\
+
+\noindent
+{\color{green} Example 1} \\
 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 $d$ irreducible polynomials in $F_q[x]$.
 For a random degree $2d-1$ polynomial $g \in F_q[x]$,
 the chance of
 $$ GCD(g^{(q^d-1)/2}-1,f_1 f_2) = f_1 \,\mbox{or}\, f_2 $$
@@ -142,14 +214,14 @@ $$ \frac{1}{2}-\frac{1}{(2q)^d}. $$
 \begin{picture}(20,14)(0,0)
 \put(7,12){\framebox(4,1.5){client}}
 \put(2,6){\framebox(4,1.5){server}}
-\put(7,6){\framebox(4,1.5){server}}
+%%\put(7,6){\framebox(4,1.5){server}}
 \put(12,6){\framebox(4,1.5){server}}
 \put(0,0){\framebox(4,1.5){server}}
 \put(5,0){\framebox(4,1.5){server}}
 \put(13.5,0){\framebox(4,1.5){server}}
 
 \put(9,12){\vector(-1,-1){4.3}}
-\put(9,12){\vector(0,-1){4.3}}
+%%\put(9,12){\vector(0,-1){4.3}}
 \put(9,12){\vector(1,-1){4.3}}
 \put(4,6){\vector(-1,-2){2.2}}
 \put(4,6){\vector(1,-2){2.2}}
@@ -195,60 +267,50 @@ def c_z(F,E,Level)
 }
 \end{verbatim}
 \newpage
-\noindent
-{\color{red} 5. e-Bateman project} \\
-First Step: \\
-Gauss Hypergeometric function:
-$$ {\color{blue} F(a,b,c;x)} = \sum_{n=1}^\infty
-  \frac{(a)_n (b)_n}{(1)_n}{(c)_n} x^n
-$$
-where
-$$ (a)_n = a(a+1) \cdots (a+n-1). $$
-$$ F(?,?,?;x) = \log (1+x). $$
 
-\noindent
-Appell's $F_1$:
-$$ {\color{blue} F_1(a,b,b',c;x,y)} = \sum_{m,n=1}^\infty
-  \frac{(a)_{m+n} (b)_m (b')_n}{(c)_{m+n}(1)_m (1)_n} x^m y^n.
-$$
-\newpage
-Mathematical formula book, e.g.,
-Erdelyi: {\color{green} Higher Transcendental Functions} \\
-{\color{blue} Formula (type A)}\\
-The solution space of the ordinary differential equation
-$$ x(1-x) \frac{d^2f}{dx^2} -\left( c-(a+b+1)x \right) \frac{df}{dx} - a b f = 0$$
-is spanned by
-$$ F(a,b,c;x) , \  x^{1-c} F(a,b,c;x) $$
-when $c \not\in {\bf Z}$. \\
-{\color{blue} Formula (type B)}\\
-\begin{eqnarray*}
-&\ & F(a_1, a_2, b_2;z) \, F(-a_1,-a_2,2-b_2;z)  \\
-&+& \frac{z}{e_2}\, F'(a_1, a_2, b_2;z) \, F(-a_1,-a_2,2-b_2;z)  \\
-&-& \frac{z}{e_2}\, F(a_1, a_2, b_2;z) \, F'(-a_1,-a_2,2-b_2;z)  \\
-&-& \frac{a_1+a_2-e_2}{a_1 a_2 e_2}z^2\,
-  F'(a_1, a_2, b_2;z)\,F'(-a_1,-a_2,2-b_2;z) \\
-&=& 1
-\end{eqnarray*}
-where $e_2 = b_2-1$ and $a_1, a_2, e_2, e_2-a_2 \not\in {\bf Z}$.  \\
-(generalization of $\sin^2 x + \cos^2 x =1$.)
+\epsfxsize=17cm
+\epsffile{cz.ps}
 
 \noindent
-Project in progress: \\
-We are trying to generate or verify type A formulas and type B formulas
-for {\color{blue} GKZ hypergeometric systems}.
+{\color{blue} Performance of parallel CZ algorithm} \\
+$d=1$, $k=200$ : product of $200$ linear forms. \\
+$d=2$, $k=50$ : product of $50$ irreducible degree $2$ polynomials. \\
 
-\begin{tabular}{|c|c|c|}
-\hline
-  & type A & type B \\ \hline
-Algorithm &  {\color{red} OK} (SST book) &  in progress \\ \hline
-Implementation & partially done & NO \\ \hline
-\end{tabular}
+\newpage
+{\color{green} Example 2} \\
+Shoup's algorithm to multiply polynomials.  \\
+{\color{green} Example 3} \\
+Competitive Gr\"obner basis computation. \\
+\newpage
 
 \noindent
-Our ox servers
-{\tt ox\_asir}, {\tt ox\_sm1}, {\tt ox\_tigers}, {\tt ox\_gnuplot},
-{\tt ox\_mathematica}, {\tt OMproxy} {\tt ox\_m2}
-are used to generate, verify and present formulas of type A
-for GKZ hypergeometric systems.
+{\color{green} Example 3. Competitive Gr\"obner Basis Computation}
+\begin{verbatim}
+extern Proc1,Proc2$
+Proc1 = -1$ Proc2 = -1$
+/* G:set of polys; V:list of variables */
+/* Mod: the Ground field GF(Mod); O:type of order */
+def dgr(G,V,Mod,O)
+{
+  /* invoke servers if necessary */
+  if ( Proc1 == -1 ) Proc1 = ox_launch();
+  if ( Proc2 == -1 ) Proc2 = ox_launch();
+  P = [Proc1,Proc2];
+  map(ox_reset,P); /* reset servers */
+  /* P0 executes Buchberger algorithm over GF(Mod) */
+  ox_cmo_rpc(P[0],"dp_gr_mod_main",G,V,0,Mod,O);
+  /* P1 executes F4 algorithm over GF(Mod) */
+  ox_cmo_rpc(P[1],"dp_f4_mod_main",G,V,Mod,O);
+  map(ox_push_cmd,P,262); /* 262 = OX_popCMO */
+  F = ox_select(P); /* wait for data */
+  /* F[0] is a server's id which is ready */
+  R = ox_get(F[0]);
+  if ( F[0] == P[0] ) { Win = "Buchberger"; Lose = P[1]; }
+  else { Win = "F4"; Lose = P[0]; }
+  ox_reset(Lose); /* reset the loser */
+  return [Win,R];
+}
+\end{verbatim}
+\newpage
 
 \end{document}
\ No newline at end of file