===================================================================
RCS file: /home/cvs/OpenXM/doc/ascm2001p/ohp.tex,v
retrieving revision 1.4
retrieving revision 1.5
diff -u -p -r1.4 -r1.5
--- OpenXM/doc/ascm2001p/ohp.tex	2001/09/25 02:28:27	1.4
+++ OpenXM/doc/ascm2001p/ohp.tex	2001/09/29 08:33:41	1.5
@@ -1,4 +1,4 @@
-%% $OpenXM: OpenXM/doc/ascm2001p/ohp.tex,v 1.3 2001/09/25 01:17:08 takayama Exp $
+%% $OpenXM: OpenXM/doc/ascm2001p/ohp.tex,v 1.4 2001/09/25 02:28:27 takayama Exp $
 \documentclass{slides}
 %%\documentclass[12pt]{article}
 \usepackage{color}
@@ -44,7 +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}
@@ -136,9 +136,72 @@ 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 $d$ irreducible polynomials in $F_q[x]$.
@@ -151,14 +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}}
@@ -220,68 +283,6 @@ Shoup's algorithm to multiply polynomials.  \\
 Competitive Gr\"obner basis computation. \\
 \newpage
 
-\noindent
-{\color{red} 5. 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 OMproxy} (JavaClasses), {\tt ox\_m2}
-are used to generate, verify and present formulas of type A
-for GKZ hypergeometric systems.
-
-\newpage
 \noindent
 {\color{green} Example 3. Competitive Gr\"obner Basis Computation}
 \begin{verbatim}