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-% $OpenXM$
-\documentstyle[epsf]{slides}
-\newtheorem{df}{Definition}
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-\newtheorem{co}[df]{Corollary}
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+% $OpenXM: OpenXM/doc/Papers/dag-noro.tex,v 1.4 2001/10/12 02:58:35 noro Exp $ 
+\documentclass{slides}
+\usepackage{color}
+\usepackage{rgb}
+\usepackage{graphicx}
+\usepackage{epsfig}
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+\def\tc{\color{red}}
+\def\fbc{\bf\color{MediumBlue}}
+\def\itc{\color{brown}}
+\def\urlc{\bf\color{DarkGreen}}
+\def\bc{\color{LightGoldenrod1}}
 
-\title{Introduction of a computer algebra system/library Risa/Asir}
+\title{\tc A computer algebra system Risa/Asir and OpenXM}
 
-\author{Masayuki Noro\\ Kobe University}
+\author{Masayuki Noro\\ Kobe University, Japan}
 \begin{document}
 \setlength{\parskip}{10pt}
 \maketitle
-\blackandwhite{dagb-noro.tex}
-\end{document}
 
+%\begin{slide}{}
+%\begin{center}
+%\fbox{\fbc \large Part I : OpenXM and Risa/Asir --- overview and history}
+%\end{center}
+%\end{slide}
+
+%\begin{slide}{}
+%\fbox{\fbc Integration of mathematical software systems}
+%
+%\begin{itemize}
+%\item Data integration
+%
+%\begin{itemize}
+%\item OpenMath ({\urlc \tt http://www.openmath.org}) , MP [GRAY98]
+%\end{itemize}
+%
+%Standards for representing mathematical objects
+%
+%\item Control integration
+%
+%\begin{itemize}
+%\item MCP [WANG99], OMEI [LIAO01]
+%\end{itemize}
+%
+%Protocols for remote subroutine calls or session management
+%
+%\item Combination of two integrations
+%
+%\begin{itemize}
+%\item MathLink, OpenMath+MCP, MP+MCP
+%
+%and OpenXM ({\urlc \tt http://www.openxm.org})
+%\end{itemize}
+%
+%Both are necessary for practical implementation
+%
+%\end{itemize}
+%\end{slide}
+\begin{slide}{}
+\fbox{\fbc A computer algebra system Risa/Asir}
+
+\begin{itemize}
+\item {\itc Software mainly for polynomial computation}
+
+Polynomial factorization, Groebner basis computation
+\item {\itc User language with C-like syntax}
+
+C language without type declaration, with list processing
+
+\item {\itc Builtin {\tt gdb}-like debugger for user programs}
+
+\item {\itc Open source} ({\urlc \tt http://www.math.kobe-u.ac.jp/Asir/asir.html})
+
+The source and binaries are available via ftp or CVS
+
+See {\urlc \tt http://www.openxm.org} to get the latest version
+
+\item {\itc OpenXM interface}
+
+\begin{itemize}
+\item OpenXM ({\urlc \tt http://www.openxm.org})
+
+An infrastructure for exchanging mathematical data
+\item Risa/Asir is a main client in OpenXM package
+\item {\tt ox\_asir} is an OpenXM server
+\item {\tt libasir.a} provides OpenXM interface via function call
+\end{itemize}
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Goal of developing Risa/Asir}
+
+\begin{itemize}
+\item {\itc Testing new algorithms}
+
+\begin{itemize}
+\item Development started in Fujitsu labs
+
+Polynomial factorization, Groebner basis related computation,
+cryptosystems , quantifier elimination , $\ldots$
+\end{itemize}
+
+\item {\itc To be a general purpose, open system}
+
+Since 1997, we have been developing OpenXM package
+containing various servers and clients
+
+Risa/Asir is a component of OpenXM
+
+\item {\itc Environment for parallel and distributed computation}
+
+\end{itemize}
+\end{slide}
+
+%\begin{slide}{}
+%\fbox{\fbc Capability for polynomial computation}
+%
+%\begin{itemize}
+%\item Fundamental polynomial arithmetics
+%
+%recursive representation and distributed representation
+%
+%\item Polynomial factorization
+%
+%\begin{itemize}
+%\item Univariate : over {\bf Q}, algebraic number fields and finite fields
+%
+%\item Multivariate : over {\bf Q}
+%\end{itemize}
+%
+%\item Groebner basis computation
+%
+%\begin{itemize}
+%\item Buchberger and $F_4$ [FAUG99] algorithm
+%
+%\item Change of ordering/RUR [ROUI96] of 0-dimensional ideals
+%
+%\item Primary ideal decomposition
+%
+%\item Computation of $b$-function (in Weyl Algebra)
+%\end{itemize}
+%\end{itemize}
+%\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc History of development : Polynomial factorization}
+
+\begin{itemize}
+\item {\itc 1989}
+
+Start of Risa/Asir with Boehm's conservative GC 
+
+({\urlc \tt http://www.hpl.hp.com/personal/Hans\_Boehm/gc})
+
+\item {\itc 1989-1992}
+
+Univariate and multivariate factorizers over {\bf Q}
+
+\item {\itc 1992-1994}
+
+Univariate factorization over algebraic number fields
+
+Intensive use of successive extension, non-squarefree norms
+
+Application to splitting field and Galois group computation
+
+\item {\itc 1996-1998}
+
+Univariate factorization over large finite fields
+
+Motivated by a reseach project in Fujitsu on cryptography
+
+\item {\itc 2000-current}
+
+Multivariate factorization over small finite fields (in progress)
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc History of development : Groebner basis}
+
+\begin{itemize}
+\item {\itc 1992-1994}
+
+User language $\Rightarrow$ C version; trace lifting [TRAV88]
+
+\item {\itc 1994-1996}
+
+Trace lifting with homogenization
+
+Omitting GB check by compatible prime [NOYO99]
+
+Modular change of ordering/RUR[ROUI96] [NOYO99]
+
+Primary ideal decomposition [SHYO96]
+
+\item {\itc 1996-1998}
+
+Efficient content reduction during NF computation [NORO97]
+Solved {\it McKay} system for the first time
+
+\item {\itc 1998-2000}
+
+Test implementation of $F_4$ [FAUG99]
+
+\item {\itc 2000-current}
+
+Buchberger algorithm in Weyl algebra
+
+Efficient $b$-function computation[OAKU97] by a modular method
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Timing data --- Factorization}
+
+\underline{\itc Univariate; over {\bf Q}}
+
+$N_{i,j}$ : a norm of a polynomial, $\deg(N_i) = i$ with $j$ modular factor
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|} \hline
+		& $N_{105,23}$ & $N_{120,20}$ & $N_{168,24}$ & $N_{210,54}$ \\ \hline
+{\tc Asir} 	& {\tc 0.86}	& {\tc 59} & {\tc 840} & {\tc hard} \\ \hline
+Asir NormFactor & 1.6 	& 2.2& 6.1& hard \\ \hline
+%Singular& hard?	& hard?& hard? & hard? \\ \hline
+CoCoA 4 & 0.2 	& 7.1	& 16 & 0.5 \\ \hline\hline
+NTL-5.2	& 0.16 	& 0.9 	& 1.4 & 0.4 \\ \hline
+\end{tabular}
+\end{center}
+
+\underline{\itc Multivariate; over {\bf Q}}
+
+$W_{i,j,k} = Wang[i]\cdot Wang[j]\cdot Wang[k]$ in {\tt asir2000/lib/fctrdata}
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|c|} \hline
+	& $W_{1,2,3}$ & $W_{4,5,6}$ & $W_{7,8,9}$ & $W_{10,11,12}$ & $W_{13,14,15}$ \\ \hline
+variables & 3 & 5 & 5 & 5 & 4 \\ \hline
+monomials & 905 & 41369 & 51940 & 30988 & 3344 \\ \hline\hline
+{\tc Asir} 	& {\tc 0.2} & {\tc 4.7} & {\tc 14} & {\tc 17} & {\tc 0.4} \\ \hline
+%Singular& $>$15min 	& ---	& ---& ---& ---\\ \hline
+CoCoA 4 & 5.2 & $>$15min 	& $>$15min & $>$15min & 117 \\ \hline\hline
+Mathematica 4& 0.2 	& 16 	& 23 & 36 & 1.1 \\ \hline
+Maple 7& 0.5 	& 18 	& 967  & 48 & 1.3 \\ \hline
+\end{tabular}
+\end{center}
+
+%--- : not tested
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Timing data --- DRL Groebner basis computation}
+
+\underline{\itc Over $GF(32003)$}
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|c|c|c|} \hline
+		& $C_7$ & $C_8$ & $K_7$ & $K_8$ & $K_9$ & $K_{10}$ & $K_{11}$ \\ \hline
+{\tc Asir $Buchberger$}	& {\tc 31} & {\tc 1687}  & {\tc 2.6}  & {\tc 27} & {\tc 294}  & {\tc 4309} & --- \\ \hline
+Singular & 8.7 & 278 & 0.6 & 5.6 & 54 & 508 & 5510 \\ \hline
+CoCoA 4 & 241 & $>$ 5h & 3.8 & 35 & 402 &7021  & --- \\ \hline\hline
+{\tc Asir $F_4$} 	& {\tc 5.3} & {\tc 129} & {\tc 0.5}  & {\tc 4.5} & {\tc 31}  & {\tc 273} & {\tc 2641} \\ \hline
+FGb(estimated)	& 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \\ \hline
+\end{tabular}
+\end{center}
+
+\underline{\itc Over {\bf Q}}
+
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|c|} \hline
+		& $C_7$ & $Homog. C_7$ & $K_7$ & $K_8$ & $McKay$ \\ \hline
+{\tc Asir $Buchberger$} 	& {\tc 389} & {\tc 594} & {\tc 29} & {\tc 299} & {\tc 34950} \\ \hline
+Singular & --- & 15247 & 7.6 & 79 & $>$ 20h \\ \hline
+CoCoA 4 & --- & 13227 & 57 & 709 & --- \\ \hline\hline
+{\tc Asir $F_4$} 	&  {\tc 989} & {\tc 456} & {\tc 90} & {\tc 991} & {\tc 4939} \\ \hline
+FGb(estimated)	& 8 &11 & 0.6 & 5 & 10 \\ \hline
+\end{tabular}
+\end{center}
+--- : not tested
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Summary of performance}
+
+\begin{itemize}
+\item {\itc Factorizer}
+
+\begin{itemize}
+\item Multivariate : reasonable performance
+
+\item Univariate : obsoleted by M. van Hoeij's new algorithm [HOEI00]
+\end{itemize}
+
+\item {\itc Groebner basis computation}
+
+\begin{itemize}
+\item Buchberger
+
+Singular shows nice perfomance
+
+Trace lifting is efficient in some cases over {\bf Q}
+
+\item $F_4$
+
+FGb is much faster than Risa/Asir
+
+But we observe that {\it McKay} is computed efficiently by $F_4$
+\end{itemize}
+\end{itemize}
+
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc What is the merit to use Risa/Asir?}
+
+\begin{itemize}
+\item {\itc Total performance is not excellent, but not bad}
+
+\item {\itc A completely open system}
+
+The whole source is available
+
+\item {\itc It serves as a test bench to try new ideas}
+
+Interactive debugger is very useful
+
+\item {\itc Interface compliant to OpenXM RFC-100}
+
+The interface is fully documented
+
+\end{itemize}
+
+\end{slide}
+
+
+%\begin{slide}{}
+%\fbox{\fbc CMO = Serialized representation of mathematical object}
+%
+%\begin{itemize}
+%\item primitive data
+%\begin{eqnarray*}
+%\mbox{Integer32} &:& ({\tt CMO\_INT32}, {\sl int32}\ \mbox{n}) \\
+%\mbox{Cstring}&:& ({\tt CMO\_STRING},{\sl int32}\,  \mbox{ n}, {\sl string}\, \mbox{s}) \\
+%\mbox{List} &:& ({\tt CMO\_LIST}, {\sl int32}\, len, ob[0], \ldots,ob[m-1])
+%\end{eqnarray*}
+%
+%\item numbers and polynomials
+%\begin{eqnarray*}
+%\mbox{ZZ}         &:& ({\tt CMO\_ZZ},{\sl int32}\, {\rm f}, {\sl byte}\, \mbox{a[1]}, \ldots
+%{\sl byte}\, \mbox{a[$|$f$|$]} ) \\
+%\mbox{Monomial32}&:& ({\tt CMO\_MONOMIAL32}, n, \mbox{e[1]}, \ldots, \mbox{e[n]}, \mbox{Coef}) \\
+%\mbox{Coef}&:& \mbox{ZZ} | \mbox{Integer32} \\
+%\mbox{Dpolynomial}&:& ({\tt CMO\_DISTRIBUTED\_POLYNOMIAL},\\
+%                  & & m, \mbox{DringDefinition}, \mbox{Monomial32}, \ldots)\\
+%\mbox{DringDefinition}
+%                  &:& \mbox{DMS of N variables} \\
+%                  & & ({\tt CMO\_RING\_BY\_NAME}, name) \\
+%                  & & ({\tt CMO\_DMS\_GENERIC}) \\
+%\end{eqnarray*}
+%\end{itemize}
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{\fbc Stack based communication}
+%
+%\begin{itemize}
+%\item Data arrived a client
+%
+%Pushed to the stack
+%
+%\item Result
+%
+%Pushd to the stack
+%
+%Written to the stream when requested by a command
+%
+%\item The reason why we use the stack
+%
+%\begin{itemize}
+%\item Stack = I/O buffer for (possibly large) objects
+%
+%Multiple requests can be sent before their execution
+%
+%A server does not get stuck in sending results
+%\end{itemize}
+%\end{itemize}
+%\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc OpenXM (Open message eXchange protocol for Mathematics) }
+
+\begin{itemize}
+\item {\itc An environment for parallel distributed computation}
+
+Both for interactive, non-interactive environment
+
+\item {\itc OpenXM RFC-100 = Client-server architecture}
+
+Client $\Leftarrow$ OX (OpenXM) message $\Rightarrow$ Server
+
+OX (OpenXM) message : command and data
+
+\item {\itc Data}
+
+Encoding : CMO (Common Mathematical Object format)
+
+Serialized representation of mathematical object
+
+--- Main idea was borrowed from OpenMath 
+
+({\urlc \tt http://www.openmath.org})
+
+\item {\itc Command}
+
+stack machine command --- server is a stackmachine
+
++ server's own command sequences --- hybrid server
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Example of distributed computation --- $F_4$ vs. $Buchberger$ }
+
+\begin{verbatim}
+/* competitive Gbase computation over GF(M) */
+/* Cf. A.28 in SINGULAR Manual */
+/* Process list is specified as buch_vs_f4_mod(...|proc=P) */
+def buch_vs_f4_mod(G,V,M,O)
+{
+  P = getopt(proc);
+  if ( type(P) == -1 ) return dp_f4_mod_main(G,V,M,O);
+  P0 = P[0]; P1 = P[1]; P = [P0,P1];
+  map(ox_reset,P); /* resets the both servers */
+  ox_cmo_rpc(P0,"dp_f4_mod_main",G,V,M,O);  /* for F4 */
+  ox_cmo_rpc(P1,"dp_gr_mod_main",G,V,0,M,O); /* for Buchberger */
+  map(ox_push_cmd,P,262); /* 262 = OX_popCMO */
+  F = ox_select(P); /* waits a server to return the result */
+  R = ox_get(F[0]); /* gets the result from the winner */
+  if ( F[0] == P0 ) { Win = "F4"; Lose = P1;}
+  else { Win = "Buchberger"; Lose = P0; }
+  ox_reset(Lose); /* simply resets the loser */
+  return [Win,R];
+}
+\end{verbatim}
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc Real speedup by parallelism --- polynomial multiplication}
+
+{\itc Product of dense univariate polynomials with 3000bit coefficients}
+
+{\itc Algorithm : FFT+Chinese remainder (by Shoup)}
+
+\epsfxsize=20cm
+\epsffile{3k.ps}
+
+{\itc Communication cost}
+
+\begin{itemize}
+\item $O(n{\color{red}\log L})$ with server-server communication (OX-RFC102)
+\item $O(n{\color{red}L})$ without server-server communication (OX-RFC100)
+\end{itemize}
+($L$: number of processes, $n$: degree)
+
+\end{slide}
+
+\begin{slide}{}
+\fbox{\fbc References}
+
+[BERN97] L. Bernardin, On square-free factorization of 
+multivariate polynomials over a finite field, Theoretical
+Computer Science 187 (1997), 105-116.
+
+[FAUG99] J.C. Faug\`ere,
+A new efficient algorithm for computing Groebner bases  ($F_4$),
+Journal of Pure and Applied Algebra (139) 1-3 (1999), 61-88.
+
+[GRAY98] S. Gray et al,
+Design and Implementation of MP, A Protocol for Efficient Exchange of
+Mathematical Expression,
+J. Symb. Comp. {\bf 25} (1998), 213-238.
+
+[HOEI00] M. van Hoeij, Factoring polynomials and the knapsack problem,
+to appear in Journal of Number Theory (2000).
+
+[LIAO01] W. Liao et al,
+OMEI: An Open Mathematical Engine Interface,
+Proc. ASCM2001 (2001), 82-91.
+[NORO97] M. Noro, J. McKay,
+Computation of replicable functions on Risa/Asir.
+Proc. PASCO'97, ACM Press (1997), 130-138.
+\end{slide}
+
+\begin{slide}{}
+
+[NOYO99] M. Noro, K. Yokoyama, 
+A Modular Method to Compute the Rational Univariate
+Representation of Zero-Dimensional Ideals.
+J. Symb. Comp. {\bf 28}/1 (1999), 243-263.
+
+[OAKU97] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
+local cohomology groups of $D$-modules.
+Advances in Applied Mathematics, 19 (1997), 61-105.
+
+[ROUI96] F. Rouillier,
+R\'esolution des syst\`emes z\'ero-dimensionnels. 
+Doctoral Thesis(1996), University of Rennes I, France.
+
+[SHYO96] T. Shimoyama, K. Yokoyama, Localization and Primary Decomposition of Polynomial Ideals.  J. Symb. Comp. {\bf 22} (1996), 247-277.
+
+[TRAV88] C. Traverso, \gr trace algorithms. Proc. ISSAC '88 (LNCS 358), 125-138.
+
+[WANG99] P. S. Wang,
+Design and Protocol for Internet Accessible Mathematical Computation,
+Proc. ISSAC '99 (1999), 291-298.
+\end{slide}
+\end{document}