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RCS file: /home/cvs/OpenXM/doc/Papers/Attic/dagb-noro.tex,v
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retrieving revision 1.7
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--- OpenXM/doc/Papers/Attic/dagb-noro.tex	2001/10/04 08:22:20	1.4
+++ OpenXM/doc/Papers/Attic/dagb-noro.tex	2001/10/10 06:32:10	1.7
@@ -1,409 +1,378 @@
-% $OpenXM: OpenXM/doc/Papers/dagb-noro.tex,v 1.3 2001/10/04 08:16:26 noro Exp $
+% $OpenXM: OpenXM/doc/Papers/dagb-noro.tex,v 1.6 2001/10/09 11:44:43 noro Exp $
 \setlength{\parskip}{10pt}
 
 \begin{slide}{}
 \begin{center}
-\fbox{\large Part I : Overview and history of Risa/Asir}
+\fbox{\large Part I : OpenXM and Risa/Asir --- overview and history}
 \end{center}
 \end{slide}
 
 \begin{slide}{}
-\fbox{A computer algebra system Risa/Asir}
+\fbox{Integration of mathematical software systems}
 
 \begin{itemize}
-\item Old style software for polynomial computation
+\item Data integration
 
 \begin{itemize}
-\item Domain specification is not necessary prior to computation
-\item automatic conversion of inputs into internal canonical forms
+\item OpenMath ({\tt http://www.openmath.org}) , MP [GRAY98]
 \end{itemize}
 
-\item User language with C-like syntax
+Standards for representing mathematical objects
 
+\item Control integration
+
 \begin{itemize}
-\item No type declaration of variables
-\item Builtin debugger for user programs
+\item MCP [WANG99], OMEI [LIAO01]
 \end{itemize}
 
-\item Open source
+Protocols for remote subroutine calls or session management
 
+\item Combination of two integrations
+
 \begin{itemize}
-\item Whole source tree is available via CVS
+\item MathLink, OpenMath+MCP, MP+MCP
+
+and OpenXM ({\tt http://www.openxm.org})
 \end{itemize}
 
-\item OpenXM ((Open message eXchange protocol for Mathematics) interface
+Both are necessary for practical implementation
 
-\begin{itemize}
-\item As a client : can call procedures on other OpenXM servers
-\item As a server : offers all its functionalities to OpenXM clients
-\item As a library : OpenXM functionality is available via subroutine calls
 \end{itemize}
-\end{itemize}
 \end{slide}
-
 \begin{slide}{}
-\fbox{Major functionalities}
+\fbox{OpenXM (Open message eXchange protocol for Mathematics) }
 
 \begin{itemize}
-\item Fundamental polynomial arithmetics
+\item An environment for parallel distributed computation
 
-\begin{itemize}
-\item Internal form of a polynomial : recursive representaion or distributed
-representation
-\end{itemize}
+Both for interactive, non-interactive environment
 
-\item Polynomial factorization
+\item Client-server architecture
 
-\begin{itemize}
-\item Univariate factorization over the rationals, algebraic number fields and various finite fields
+Client $\Leftarrow$ OX (OpenXM) message $\Rightarrow$ Server
 
-\item Multivariate factorization over the rationals
-\end{itemize}
+OX (OpenXM) message : command and data
 
-\item Groebner basis computation
+\item Data
 
-\begin{itemize}
-\item Buchberger and $F_4$ [Faug\'ere] algorithm
+Encoding : CMO (Common Mathematical Object format)
 
-\item Change of ordering/RUR [Rouillier] of 0-dimensional ideals
+Serialized representation of mathematical object
 
-\item Primary ideal decomposition
+--- Main idea was borrowed from OpenMath
+\item Command
 
-\item Computation of $b$-function
-\end{itemize}
+stack machine command --- server is a stackmachine
 
-\item PARI [PARI] library interface 
-
-\item Paralell distributed computation under OpenXM 
++ server's own command sequences --- hybrid server
 \end{itemize}
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : ---1994}
+\fbox{A computer algebra system Risa/Asir}
 
-\begin{itemize}
-\item --1989
+({\tt http://www.math.kobe-u.ac.jp/Asir/asir.html})
 
-Several subroutines were developed for a Prolog program.
-
-\item 1989--1992
-
 \begin{itemize}
-\item Reconfigured as Risa/Asir with a parser and Boehm's conservative GC [Boehm]
+\item Traditional style software for polynomial computation
 
-\item Developed univariate and multivariate factorizers over the rationals.
-\end{itemize}
+No domain specification, automatic expansion
 
-\item 1992--1994
+\item User language with C-like syntax
 
-\begin{itemize}
-\item Started implementation of Buchberger algorithm
+C language without type declaration, with list processing
 
-Written in user language $\Rightarrow$ rewritten in C (by Murao)
+\item Builtin {\tt gdb}-like debugger for user programs
 
-$\Rightarrow$ trace lifting [Traverso]
+\item Open source
 
-\item Univariate factorization over algebraic number fields
+Whole source tree is available via CVS
 
-Intensive use of successive extension, non-squarefree norms
+\item OpenXM interface
+
+\begin{itemize}
+\item Risa/Asir is a main client in OpenXM package.
+\item An OpenXM server {\tt ox\_asir}
+\item A library with OpenXM library interface {\tt libasir.a}
 \end{itemize}
 \end{itemize}
-
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : 1994-1996}
+\fbox{Goal of developing Risa/Asir}
 
 \begin{itemize}
-\item Free distribution of binary versions from Fujitsu
+\item Efficient implementation in specific area
 
-\item Primary ideal decomposition
-
 \begin{itemize}
-\item Shimoyama-Yokoyama algorithm [SY]
+\item Polynomial factorization
+
+\item Groebner basis related computation
+
+Main target : coefficient swells in characteristic 0 cases
+
+Main tool : modular method
 \end{itemize}
 
-\item Improvement of Buchberger algorithm
+\item Front-end or server of a general purpose math software
 
+We do not persist in self-containedness
+
 \begin{itemize}
-\item Trace lifting+homogenization
 
-\item Omitting check by compatible prime
+\item contains PARI library ({\tt http://www.parigp-home.de}) from the very beginning
 
-\item Modular change of ordering, Modular RUR
+\item also acts as a main client of OpenXM package
 
-These are joint works with Yokoyama [NY]
+One can use various OpenXM servers
+
 \end{itemize}
-\end{itemize}
 
+\end{itemize}
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : 1996-1998}
+\fbox{Capability for polynomial computation}
 
 \begin{itemize}
-\item Distributed compuatation
+\item Fundamental polynomial arithmetics
 
-\begin{itemize}
-\item A prototype of OpenXM
-\end{itemize}
+recursive representation and distributed representation
 
-\item Improvement of Buchberger algorithm
+\item Polynomial factorization
 
 \begin{itemize}
-\item Content reduction during nomal form computation
+\item Univariate : over {\bf Q}, algebraic number fields and finite fields
 
-\item Its parallelization by the above facility
-
-\item Computation of odd order replicable functions [Noro]
-
-Risa/Asir : it took 5days to compute a DRL basis ({\it McKay})
-
-Faug\`ere FGb : computation of the DRL basis 53sec
+\item Multivariate : over {\bf Q}
 \end{itemize}
 
+\item Groebner basis computation
 
-\item Univariate factorization over large finite fields
-
 \begin{itemize}
-\item To implement Schoof-Elkies-Atkin algorithm 
+\item Buchberger and $F_4$ [FAUG99] algorithm
 
-Counting rational points on elliptic curves
+\item Change of ordering/RUR [ROUI96] of 0-dimensional ideals
 
---- not free But related functions are freely available
+\item Primary ideal decomposition
+
+\item Computation of $b$-function (in Weyl Algebra)
 \end{itemize}
 \end{itemize}
-
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : 1998-2000}
-\begin{itemize}
-\item OpenXM
+\fbox{History of development : Polynomial factorization}
 
 \begin{itemize}
-\item OpenXM specification was written by Noro and Takayama
+\item 1989
 
-Borrowed idea on encoding, phrase book from OpenMath [OpenMath]
+Start of Risa/Asir with Boehm's conservative GC 
 
-\item Functions for distributed computation were rewritten
-\end{itemize}
+({\tt http://www.hpl.hp.com/personal/Hans\_Boehm/gc})
 
-\item Risa/Asir on Windows
+\item 1989-1992
 
-\begin{itemize}
-\item Requirement from a company for which Noro worked
+Univariate and multivariate factorizers over {\bf Q}
 
-Written in Visual C++
-\end{itemize}
+\item 1992-1994
 
-\item Test implementation of $F_4$
+Univariate factorization over algebraic number fields
 
-\begin{itemize}
-\item Implemented according to [Faug\`ere]
+Intensive use of successive extension, non-squarefree norms
 
-\item Over $GF(p)$ : pretty good
+\item 1996-1998
 
-\item Over the rationals : not so good except for {\it McKay}
+Univariate factorization over large finite fields
+
+\item 2000-current 
+
+Multivariate factorization over small finite fields (in progress)
 \end{itemize}
-\end{itemize}
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : 2000-current}
-\begin{itemize}
-\item The source code is freely available
+\fbox{History of development : Groebner basis}
 
 \begin{itemize}
-\item Noro moved from Fujitsu to Kobe university
+\item 1992-1994
 
-Started Kobe branch [Risa/Asir]
-\end{itemize}
+User language $\Rightarrow$ C version; trace lifting [TRAV88]
 
-\item OpenXM [OpenXM]
+\item 1994-1996
 
-\begin{itemize}
-\item Revising the specification : OX-RFC100, 101, (102)
+Trace lifting with homogenization
 
-\item OX-RFC102 : communications between servers via MPI
-\end{itemize}
+Omitting GB check by compatible prime [NOYO99]
 
-\item Weyl algebra
+Modular change of ordering/RUR [NOYO99]
 
-\begin{itemize}
-\item Buchberger algorithm [Takayama]
+Primary ideal decomposition [SHYO96]
 
-\item $b$-function computation [Oaku]
+\item 1996-1998
 
-Minimal polynomial computation by modular method
-\end{itemize}
-\end{itemize}
+Efficient content reduction during NF computation [NORO97]
+Solved {\it McKay} system for the first time
 
+\item 1998-2000
+
+Test implementation of $F_4$
+
+\item 2000-current
+
+Buchberger algorithm in Weyl algebra [TAKA90]
+
+Efficient $b$-function computation by a modular method
+\end{itemize}
 \end{slide}
 
 \begin{slide}{}
-\fbox{Status of each component --- Factorizer}
+\fbox{Performance --- Factorizer}
 
 \begin{itemize}
-\item 10 years ago
-
-its performace was fine compared with existing software
-like REDUCE, Mathematica.
-
 \item 4 years ago
 
-Univarate factorization over algebraic number fields was
-still fine because of some tricks on factoring polynomials
+Over {\bf Q} : fine compared with existing software
+like REDUCE, Mathematica, maple
+
+Univariate, over algebraic number fields :
+fine because of some tricks for polynomials
 derived from norms.
 
 \item Current
 
-Multivariate : not so bad
+Multivariate : moderate
 
-Univariate : completely obsolete by M. van Hoeij's new algorithm
-[Hoeij]
+Univariate : completely obsoleted by M. van Hoeij's new algorithm
+[HOEI00]
 \end{itemize}
 
 \end{slide}
 
 \begin{slide}{}
-\fbox{Status of each component --- Groebner basis related functions}
+\fbox{Timing data --- Factorization}
 
-\begin{itemize}
-\item 8 years ago
+\underline{Univariate; over {\bf Q}}
 
-The performace was poor with only the sugar strategy.
+$N_i$ : a norm of a poly, $\deg(N_i) = i$
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|} \hline
+		& $N_{105}$ & $N_{120}$ & $N_{168}$ & $N_{210}$ \\ \hline
+Asir 	& 0.86	& 59 & 840 & 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}
 
-\item 7 years ago
+\underline{Multivariate; over {\bf Q}}
 
-Rather fine with trace lifting but Faug\`ere's (old)Gb was more
-efficient.  
+$W_{i,j,k} = Wang[i]\cdot Wang[j]\cdot Wang[k]$ 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
+Asir 	& 0.2 & 4.7 & 14 & 17 & 0.4 \\ \hline
+Singular& $>$15min 	& ---	& ---& ---& ---\\ \hline
+CoCoA 4 & 5.2 & $>$15min 	& $>$15min & $>$15min & 117 \\ \hline\hline
+Mathematica& 0.2 	& 16 	& 23 & 36 & 1.1 \\ \hline
+\end{tabular}
+\end{center}
 
-Homogenization+trace lifting made it possible to compute
-wider range of Groebner bases.
-
-\item 4 years ago
-
-Modular RUR was comparable with Rouillier's implementation.
-
-\item Current
-
-FGb seems much more efficient than our $F_4$ implementation.
-
-Singular [Singular] is also several times
-faster than Risa/Asir, because Singular seems to have efficient
-monomial and polynomial representation.
-
-\end{itemize}
+--- : not tested
 \end{slide}
-
 \begin{slide}{}
-\fbox{OpenXM}
+\fbox{Performance --- Groebner basis related computation}
 
 \begin{itemize}
-\item An environment for parallel distributed computation
+\item 7 years ago
 
-Both for interactive, non-interactive environment
+Trace lifting : rather fine but coefficient swells often occur
 
-\item Message passing
+Homogenization+trace lifting : robust and fast in the above cases
 
-OX (OpenXM) message : command and data
+\item 4 years ago
 
-\item Hybrid command execution
+Modular RUR was comparable with Rouillier's implementation.
 
-\begin{itemize}
-\item Stack machine command
+DRL basis of {\it McKay}: 
 
-push, pop, function execution, $\ldots$
+5 days on Risa/Asir, 53 seconds on Faug\`ere FGb
+\item Current
 
-\item accepts its own command sequences
+$F_4$ in FGb : much more efficient than $F_4$ in Risa/Asir
 
-{\tt execute\_string} --- easy to use
-\end{itemize}
+Buchberger in Singular ({\tt http://www.singular.uni-kl.de})
+: faster than Risa/Asir
 
-\item Data is represented as CMO
 
-CMO (Common Mathematical Object format)
+$\Leftarrow$ efficient monomial and polynomial computation
 
---- Serialized representation of mathematical object
-
-{\sl Integer32}, {\sl Cstring}, {\sl List}, {\sl ZZ}, $\ldots$
 \end{itemize}
 \end{slide}
 
-
 \begin{slide}{}
-\fbox{OpenXM and OpenMath}
+\fbox{Timing data --- DRL Groebner basis computation}
 
-\begin{itemize}
-\item OpenMath
+\underline{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
+Asir $Buchberger$ 	& 31 & 1687  & 2.6  & 27 & 294  & 4309 & --- \\ \hline
+Singular & 8.7 & 278 & 0.6 & 5.6 & 54 & 508 & 5510 \\ \hline
+CoCoA 4 & 241 & & 3.8 & 35 & 402 & & --- \\ \hline\hline
+Asir $F_4$ 	& 5.3 & 129 & 0.5  & 4.5 & 31  & 273 & 2641 \\ \hline
+FGb(estimated)	& 0.9 & 23 & 0.1 & 0.8 & 6 & 51 & 366 \\ \hline
+\end{tabular}
+\end{center}
 
-\begin{itemize}
-\item A standard for representing mathematical objects
+\underline{Over {\bf Q}}
 
-\item CD (Content Dictionary) : assigns semantics to symbols
-
-\item Phrasebook : convesion between internal and OpenMath objects.
-
-\item Encoding : format for actual data exchange
-\end{itemize}
-
-\item OpenXM
-
-\begin{itemize}
-\item Specification for encoding and exchanging messages
-
-\item It also specifies behavior of servers and session management
-\end{itemize}
-
-\end{itemize}
+\begin{center}
+\begin{tabular}{|c||c|c|c|c|c|} \hline
+		& $C_7$ & $Homog. C_7$ & $K_7$ & $K_8$ & $McKay$ \\ \hline
+Asir $Buchberger$ 	& 389 & 594 & 29 & 299 & 34950 \\ \hline
+Singular & --- & 15247 & 7.6 & 79 & $>$ 20h \\ \hline
+CoCoA 4 & --- & 13227 & 57 & 709 & --- \\ \hline\hline
+Asir $F_4$ 	&  989 & 456 & 90 & 991 & 4939 \\ \hline
+FGb(estimated)	& 8 &11 & 0.6 & 5 & 10 \\ \hline
+\end{tabular}
+\end{center}
+--- : not tested
 \end{slide}
-
 \begin{slide}{}
-\fbox{OpenXM server interface in Risa/Asir}
+\fbox{How do we proceed?}
 
-\begin{itemize}
-\item TCP/IP stream
+\underline{Total performance : not excellent, but not so bad}
 
 \begin{itemize}
-\item Launcher
+\item Trying to improve our implementation
 
-A client executes a launcher on a host.
+This is very important as a motivation of further development
 
-The launcher launches a server on the same host.
+\begin{itemize}
 
-\item Server
+\item Computation of $b$-function
 
-A server reads from the descriptor 3, write to the descriptor 4.
+fast but not satisfactory
 
+$\Rightarrow$ Groebner basis computation in Weyl
+algebra should be improved
 \end{itemize}
 
-\item Subroutine call
+\item Developing new OpenXM servers
 
-Risa/Asir subroutine library provides interfaces corresponding to
-pushing and popping data and executing stack commands.
-\end{itemize}
-\end{slide}
+{ox\_NTL} for univariate factorization, 
 
-\begin{slide}{}
-\fbox{OpenXM client interface in Risa/Asir}
+{ox\_???} for Groebner basis computation, etc.
 
-\begin{itemize}
-\item Primitive interface functions
+$\Rightarrow$ Risa/Asir can be a front-end of efficient servers
 
-Pushing and popping data, sending commands etc.
-
-\item Convenient functions
-
-Launching servers, calling remote functions,
- interrupting remote executions etc.
-
-\item Parallel distributed computation is easy
-
-Simple parallelization is practically important
-
-Competitive computation is easily realized 
 \end{itemize}
+
+\begin{center}
+\underline{In both cases, OpenXM interface is important}
+\end{center}
 \end{slide}
 
 
@@ -453,7 +422,7 @@ Competitive computation is easily realized 
 %\begin{itemize}
 %\item Stack = I/O buffer for (possibly large) objects
 %
-%Multiple requests can be sent before their exection
+%Multiple requests can be sent before their execution
 %
 %A server does not get stuck in sending results
 %\end{itemize}
@@ -461,39 +430,6 @@ Competitive computation is easily realized 
 %\end{slide}
 
 \begin{slide}{}
-\fbox{Executing functions on a server (I) --- {\tt SM\_executeFunction}}
-
-\begin{enumerate}
-\item (C $\rightarrow$ S) Arguments are sent in binary encoded form.
-\item (C $\rightarrow$ S) The number of aruments is sent as {\sl Integer32}.
-\item (C $\rightarrow$ S) A function name is sent as {\sl Cstring}.
-\item (C $\rightarrow$ S) A command {\tt SM\_executeFunction} is sent.
-\item The result is pushed to the stack.
-\item (C $\rightarrow$ S) A command {\tt SM\_popCMO} is sent.
-\item (S $\rightarrow$ C) The result is sent in binary encoded form.
-\end{enumerate}
-
-$\Rightarrow$ Communication is fast, but functions for binary data
-conversion are necessary.
-\end{slide}
-
-\begin{slide}{}
-\fbox{Executing functions on a server (II) --- {\tt SM\_executeString}}
-
-\begin{enumerate}
-\item (C $\rightarrow$ S) A character string represeting a request in a server's
-user language is sent as {\sl Cstring}.
-\item (C $\rightarrow$ S) A command {\tt SM\_executeString} is sent.
-\item The result is pushed to the stack.
-\item (C $\rightarrow$ S) A command {\tt SM\_popString} is sent.
-\item (S $\rightarrow$ C) The result is sent in readable form.
-\end{enumerate}
-
-$\Rightarrow$ Communication may be slow, but the client parser may be
-enough to read the result.
-\end{slide}
-
-\begin{slide}{}
 \fbox{Example of distributed computation --- $F_4$ vs. $Buchberger$ }
 
 \begin{verbatim}
@@ -521,53 +457,52 @@ def grvsf4(G,V,M,O)
 \begin{slide}{}
 \fbox{References}
 
-[Bernardin] L. Bernardin, On square-free factorization of 
+[BERN97] L. Bernardin, On square-free factorization of 
 multivariate polynomials over a finite field, Theoretical
 Computer Science 187 (1997), 105-116.
 
-[Boehm] {\tt http://www.hpl.hp.com/personal/Hans\_Boehm/gc}
-
-[Faug\`ere] J.C. Faug\`ere,
+[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.
 
-[Hoeij] M. van Heoij, Factoring polynomials and the knapsack problem,
+[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 Heoij, Factoring polynomials and the knapsack problem,
 to appear in Journal of Number Theory (2000).
 
-[Noro] M. Noro, J. McKay,
+[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. of PASCO'97, ACM Press, 130-138 (1997).
+Proc. PASCO'97, ACM Press (1997), 130-138.
+\end{slide}
 
-[NY] M. Noro, K. Yokoyama, 
+\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.
-\end{slide}
 
-\begin{slide}{}
-
-[Oaku] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
+[OAKU97] T. Oaku, Algorithms for $b$-functions, restrictions and algebraic
 local cohomology groups of $D$-modules.
-Advancees in Applied Mathematics, 19 (1997), 61-105.
+Advances in Applied Mathematics, 19 (1997), 61-105.
 
-[OpenMath] {\tt http://www.openmath.org}
-
-[OpenXM] {\tt http://www.openxm.org}
-
-[PARI] {\tt http://www.parigp-home.de}
-
-[Risa/Asir] {\tt http://www.math.kobe-u.ac.jp/Asir/asir.html}
-
-[Rouillier] F. Rouillier,
+[ROUI96] F. Rouillier,
 R\'esolution des syst\`emes z\'ero-dimensionnels. 
 Doctoral Thesis(1996), University of Rennes I, France.
 
-[SY] T. Shimoyama, K. Yokoyama, Localization and Primary Decomposition of Polynomial Ideals.  J. Symb. Comp. {\bf 22} (1996), 247-277.
+[SHYO96] T. Shimoyama, K. Yokoyama, Localization and Primary Decomposition of Polynomial Ideals.  J. Symb. Comp. {\bf 22} (1996), 247-277.
 
-[Singular] {\tt http://www.singular.uni-kl.de}
+[TRAV88] C. Traverso, \gr trace algorithms. Proc. ISSAC '88 (LNCS 358), 125-138.
 
-[Traverso] 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}
 
 \begin{slide}{}
@@ -619,7 +554,7 @@ Berlekamp-Zassenhaus
 
 Trager's algorithm + some improvement
 
-\item Over finite fieds
+\item Over finite fields
 
 DDF + Cantor-Zassenhaus; FFT for large finite fields
 \end{itemize}
@@ -631,9 +566,9 @@ DDF + Cantor-Zassenhaus; FFT for large finite fields
 
 Classical EZ algorithm
 
-\item Over small finite fieds
+\item Over small finite fields
 
-Modified Bernardin's square free algorithm [Bernardin],
+Modified Bernardin's square free algorithm [BERN97],
 
 possibly Hensel lifting over extension fields
 \end{itemize}
@@ -676,7 +611,7 @@ Key : an efficient implementation of Leibniz rule
 \begin{itemize}
 \item More efficient than our Buchberger algorithm implementation
 
-but less efficient than FGb by Faugere
+but less efficient than FGb by Faug\`ere
 \end{itemize}
 
 \item Over the rationals
@@ -792,6 +727,256 @@ The knapsack factorization is available via {\tt pari(
 \end{itemize}
 \end{slide}
 
+\begin{slide}{}
+\fbox{OpenXM server interface in Risa/Asir}
+
+\begin{itemize}
+\item TCP/IP stream
+
+\begin{itemize}
+\item Launcher
+
+A client executes a launcher on a host.
+
+The launcher launches a server on the same host.
+
+\item Server
+
+Reads from the descriptor 3
+
+Writes to the descriptor 4
+
+\end{itemize}
+
+\item Subroutine call
+
+In Risa/Asir subroutine library {\tt libasir.a}:
+
+OpenXM functionalities are implemented as function calls
+
+pushing and popping data, executing stack commands etc.
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{OpenXM client interface in Risa/Asir}
+
+\begin{itemize}
+\item Primitive interface functions
+
+Pushing and popping data, sending commands etc.
+
+\item Convenient functions
+
+Launching servers,
+
+Calling remote functions,
+
+Resetting remote executions etc.
+
+\item Parallel distributed computation
+
+Simple parallelization is practically important
+
+Competitive computation is easily realized ($\Rightarrow$ demo)
+\end{itemize}
+\end{slide}
+
+\begin{slide}{}
+\fbox{Executing functions on a server (I) --- {\tt SM\_executeFunction}}
+
+\begin{enumerate}
+\item (C $\rightarrow$ S) Arguments are sent in binary encoded form.
+\item (C $\rightarrow$ S) The number of arguments is sent as {\sl Integer32}.
+\item (C $\rightarrow$ S) A function name is sent as {\sl Cstring}.
+\item (C $\rightarrow$ S) A command {\tt SM\_executeFunction} is sent.
+\item The result is pushed to the stack.
+\item (C $\rightarrow$ S) A command {\tt SM\_popCMO} is sent.
+\item (S $\rightarrow$ C) The result is sent in binary encoded form.
+\end{enumerate}
+
+$\Rightarrow$ Communication is fast, but functions for binary data
+conversion are necessary.
+\end{slide}
+
+\begin{slide}{}
+\fbox{Executing functions on a server (II) --- {\tt SM\_executeString}}
+
+\begin{enumerate}
+\item (C $\rightarrow$ S) A character string representing a request in a server's
+user language is sent as {\sl Cstring}.
+\item (C $\rightarrow$ S) A command {\tt SM\_executeString} is sent.
+\item The result is pushed to the stack.
+\item (C $\rightarrow$ S) A command {\tt SM\_popString} is sent.
+\item (S $\rightarrow$ C) The result is sent in readable form.
+\end{enumerate}
+
+$\Rightarrow$ Communication may be slow, but the client parser may be
+enough to read the result.
+\end{slide}
+
+%\begin{slide}{}
+%\fbox{History of development : ---1994}
+%
+%\begin{itemize}
+%\item --1989
+%
+%Several subroutines were developed for a Prolog program.
+%
+%\item 1989--1992
+%
+%\begin{itemize}
+%\item Reconfigured as Risa/Asir with a parser and Boehm's conservative GC
+%
+%\item Developed univariate and multivariate factorizers over the rationals.
+%\end{itemize}
+%
+%\item 1992--1994
+%
+%\begin{itemize}
+%\item Started implementation of Buchberger algorithm
+%
+%Written in user language $\Rightarrow$ rewritten in C (by Murao)
+%
+%$\Rightarrow$ trace lifting [TRAV88]
+%
+%\item Univariate factorization over algebraic number fields
+%
+%Intensive use of successive extension, non-squarefree norms
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{History of development : 1994-1996}
+%
+%\begin{itemize}
+%\item Free distribution of binary versions from Fujitsu
+%
+%\item Primary ideal decomposition
+%
+%\begin{itemize}
+%\item Shimoyama-Yokoyama algorithm [SHYO96]
+%\end{itemize}
+%
+%\item Improvement of Buchberger algorithm
+%
+%\begin{itemize}
+%\item Trace lifting+homogenization
+%
+%\item Omitting check by compatible prime
+%
+%\item Modular change of ordering, Modular RUR
+%
+%These are joint works with Yokoyama [NOYO99]
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{History of development : 1996-1998}
+%
+%\begin{itemize}
+%\item Distributed computation
+%
+%\begin{itemize}
+%\item A prototype of OpenXM
+%\end{itemize}
+%
+%\item Improvement of Buchberger algorithm
+%
+%\begin{itemize}
+%\item Content reduction during normal form computation
+%
+%\item Its parallelization by the above facility
+%
+%\item Computation of odd order replicable functions [NORO97]
+%
+%Risa/Asir : it took 5days to compute a DRL basis ({\it McKay})
+%
+%Faug\`ere FGb : computation of the DRL basis 53sec
+%\end{itemize}
+%
+%
+%\item Univariate factorization over large finite fields
+%
+%\begin{itemize}
+%\item To implement Schoof-Elkies-Atkin algorithm 
+%
+%Counting rational points on elliptic curves
+%
+%--- not free But related functions are freely available
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{History of development : 1998-2000}
+%\begin{itemize}
+%\item OpenXM
+%
+%\begin{itemize}
+%\item OpenXM specification was written by Noro and Takayama
+%
+%Borrowed idea on encoding, phrase book from OpenMath
+%
+%\item Functions for distributed computation were rewritten
+%\end{itemize}
+%
+%\item Risa/Asir on Windows
+%
+%\begin{itemize}
+%\item Requirement from a company for which Noro worked
+%
+%Written in Visual C++
+%\end{itemize}
+%
+%\item Test implementation of $F_4$
+%
+%\begin{itemize}
+%\item Implemented according to [FAUG99]
+%
+%\item Over $GF(p)$ : pretty good
+%
+%\item Over the rationals : not so good except for {\it McKay}
+%\end{itemize}
+%\end{itemize}
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{History of development : 2000-current}
+%\begin{itemize}
+%\item The source code is freely available
+%
+%\begin{itemize}
+%\item Noro moved from Fujitsu to Kobe university
+%
+%Started Kobe branch
+%\end{itemize}
+%
+%\item OpenXM
+%
+%\begin{itemize}
+%\item Revising the specification : OX-RFC100, 101, (102)
+%
+%\item OX-RFC102 : communications between servers via MPI
+%\end{itemize}
+%
+%\item Weyl algebra
+%
+%\begin{itemize}
+%\item Buchberger algorithm [TAKA90]
+%
+%\item $b$-function computation [OAKU97]
+%
+%Minimal polynomial computation by modular method
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
 \begin{slide}{}
 \end{slide}