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RCS file: /home/cvs/OpenXM/doc/Papers/Attic/dagb-noro.tex,v
retrieving revision 1.4
retrieving revision 1.5
diff -u -p -r1.4 -r1.5
--- OpenXM/doc/Papers/Attic/dagb-noro.tex	2001/10/04 08:22:20	1.4
+++ OpenXM/doc/Papers/Attic/dagb-noro.tex	2001/10/09 01:44:21	1.5
@@ -1,259 +1,219 @@
-% $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 1.4 2001/10/04 08:22:20 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{OpenXM (Open message eXchange protocol for Mathematics) }
 
 \begin{itemize}
-\item Old style software for polynomial computation
+\item An environment for parallel distributed computation
 
-\begin{itemize}
-\item Domain specification is not necessary prior to computation
-\item automatic conversion of inputs into internal canonical forms
-\end{itemize}
+Both for interactive, non-interactive environment
 
-\item User language with C-like syntax
+\item Client-server architecture
 
-\begin{itemize}
-\item No type declaration of variables
-\item Builtin debugger for user programs
-\end{itemize}
+Client $\Leftarrow$ OX (OpenXM) message $\Rightarrow$ Server
 
-\item Open source
+OX (OpenXM) message : command and data
 
-\begin{itemize}
-\item Whole source tree is available via CVS
-\end{itemize}
+\item Data
 
-\item OpenXM ((Open message eXchange protocol for Mathematics) interface
+Encoding : CMO (Common Mathematical Object format)
 
-\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
+Serialized representation of mathematical object
+
+--- Main idea was borrowed from OpenMath [OpenMath]
+\item Command
+
+stack machine command --- server is a stackmachine
+
++ server's own command sequences --- hybrid server
 \end{itemize}
-\end{itemize}
 \end{slide}
 
+
 \begin{slide}{}
-\fbox{Major functionalities}
+\fbox{OpenXM and OpenMath}
 
 \begin{itemize}
-\item Fundamental polynomial arithmetics
+\item OpenMath
 
 \begin{itemize}
-\item Internal form of a polynomial : recursive representaion or distributed
-representation
-\end{itemize}
+\item A standard for representing mathematical objects
 
-\item Polynomial factorization
+\item CD (Content Dictionary) : assigns semantics to symbols
 
-\begin{itemize}
-\item Univariate factorization over the rationals, algebraic number fields and various finite fields
+\item Phrasebook : convesion between internal and OpenMath objects.
 
-\item Multivariate factorization over the rationals
+\item Encoding : format for actual data exchange
 \end{itemize}
 
-\item Groebner basis computation
+\item OpenXM
 
 \begin{itemize}
-\item Buchberger and $F_4$ [Faug\'ere] algorithm
+\item Specification for encoding and exchanging messages
 
-\item Change of ordering/RUR [Rouillier] of 0-dimensional ideals
-
-\item Primary ideal decomposition
-
-\item Computation of $b$-function
+\item It also specifies behavior of servers and session management
 \end{itemize}
 
-\item PARI [PARI] library interface 
-
-\item Paralell distributed computation under OpenXM 
 \end{itemize}
 \end{slide}
-
 \begin{slide}{}
-\fbox{History of development : ---1994}
+\fbox{A computer algebra system Risa/Asir}
 
 \begin{itemize}
-\item --1989
+\item Old style software for polynomial computation
 
-Several subroutines were developed for a Prolog program.
+No domain specification, automatic expansion
 
-\item 1989--1992
+\item User language with C-like syntax
 
-\begin{itemize}
-\item Reconfigured as Risa/Asir with a parser and Boehm's conservative GC [Boehm]
+C language without type declaration, with list processing
 
-\item Developed univariate and multivariate factorizers over the rationals.
-\end{itemize}
+\item Builtin {\tt gdb}-like debugger for user programs
 
-\item 1992--1994
+\item Open source
 
-\begin{itemize}
-\item Started implementation of Buchberger algorithm
+Whole source tree is available via CVS
 
-Written in user language $\Rightarrow$ rewritten in C (by Murao)
+\item OpenXM interface
 
-$\Rightarrow$ trace lifting [Traverso]
-
-\item Univariate factorization over algebraic number fields
-
-Intensive use of successive extension, non-squarefree norms
+\begin{itemize}
+\item Risa/Asir is a main client in OpenXM package.
+\item An OpenXM server {\tt ox\_asir}
+\item An library with OpemXM library inteface {\tt libasir.a}
 \end{itemize}
 \end{itemize}
-
 \end{slide}
 
 \begin{slide}{}
-\fbox{History of development : 1994-1996}
+\fbox{Aim of developing Risa/Asir}
 
 \begin{itemize}
-\item Free distribution of binary versions from Fujitsu
+\item Efficient implementation in specific area
 
-\item Primary ideal decomposition
+Polynomial factorization, Groebner basis related computation
 
-\begin{itemize}
-\item Shimoyama-Yokoyama algorithm [SY]
-\end{itemize}
+$\Rightarrow$ serves as an OpenXM server/library
 
-\item Improvement of Buchberger algorithm
+\item Front-end of a general purpose math software
 
-\begin{itemize}
-\item Trace lifting+homogenization
+Risa/Asir contains PARI library [PARI] from the very beginning
 
-\item Omitting check by compatible prime
+It also acts as a main client of OpenXM package
 
-\item Modular change of ordering, Modular RUR
-
-These are joint works with Yokoyama [NY]
 \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 representaion 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 $F_4$ [Faug\'ere] algorithm
 
-Counting rational points on elliptic curves
+\item Change of ordering/RUR [Rouillier] 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 [Boehm]
 
-\item Functions for distributed computation were rewritten
-\end{itemize}
+\item 1989-1992
 
-\item Risa/Asir on Windows
+Univariate and multivariate factorizers over {\bf Q}
 
-\begin{itemize}
-\item Requirement from a company for which Noro worked
+\item 1992-1994
 
-Written in Visual C++
-\end{itemize}
+Univariate factorization over algebraic number fields
 
-\item Test implementation of $F_4$
+Intensive use of successive extension, non-squarefree norms
 
-\begin{itemize}
-\item Implemented according to [Faug\`ere]
+\item 1996-1998
 
-\item Over $GF(p)$ : pretty good
+Univariate factorization over large finite fields
 
-\item Over the rationals : not so good except for {\it McKay}
+\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 [Traverso]
 
-\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 [NY]
 
-\item Weyl algebra
+Modular change of ordering/RUR [NY]
 
-\begin{itemize}
-\item Buchberger algorithm [Takayama]
+Primary ideal decompositon [SY]
 
-\item $b$-function computation [Oaku]
+\item 1996-1998
 
-Minimal polynomial computation by modular method
-\end{itemize}
-\end{itemize}
+Effifcient content reduction during NF computation and its parallelization
+[Noro] (Solved {\it McKay} system for the first time)
 
+\item 1998-2000
+
+Test implementation of $F_4$
+
+\item 2000-current
+
+Buchberger algorithm in Weyl algebra [Takayama]
+
+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
+
+Univarate, over algebraic number fields :
+fine because of some tricks for polynomials
 derived from norms.
 
 \item Current
@@ -267,96 +227,57 @@ Univariate : completely obsolete by M. van Hoeij's new
 \end{slide}
 
 \begin{slide}{}
-\fbox{Status of each component --- Groebner basis related functions}
+\fbox{Performance --- Groebner basis related computation}
 
 \begin{itemize}
-\item 8 years ago
-
-The performace was poor with only the sugar strategy.
-
 \item 7 years ago
 
-Rather fine with trace lifting but Faug\`ere's (old)Gb was more
-efficient.  
+Trace lifting : rather fine but coefficient swells often occur
 
-Homogenization+trace lifting made it possible to compute
-wider range of Groebner bases.
+Homogenization+trace lifting : robust and fast in the above cases
 
 \item 4 years ago
 
 Modular RUR was comparable with Rouillier's implementation.
 
+DRL basis of {\it McKay}: 
+
+5 days on Risa/Asir, 53 seconds on Faugere FGb
 \item Current
 
-FGb seems much more efficient than our $F_4$ implementation.
+$F_4$ in FGb : much more efficient than $F_4$ in Risa/Asir
 
-Singular [Singular] is also several times
-faster than Risa/Asir, because Singular seems to have efficient
-monomial and polynomial representation.
+Buchberger in Singular [Singular] : faster than Risa/Asir
 
-\end{itemize}
-\end{slide}
+$\Leftarrow$ efficient monomial and polynomial representation
 
-\begin{slide}{}
-\fbox{OpenXM}
-
-\begin{itemize}
-\item An environment for parallel distributed computation
-
-Both for interactive, non-interactive environment
-
-\item Message passing
-
-OX (OpenXM) message : command and data
-
-\item Hybrid command execution
-
-\begin{itemize}
-\item Stack machine command
-
-push, pop, function execution, $\ldots$
-
-\item accepts its own command sequences
-
-{\tt execute\_string} --- easy to use
 \end{itemize}
-
-\item Data is represented as CMO
-
-CMO (Common Mathematical Object format)
-
---- 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{How do we proceed?}
 
 \begin{itemize}
-\item OpenMath
+\item Developing new OpenXM servers
 
-\begin{itemize}
-\item A standard for representing mathematical objects
+{ox\_NTL} for univariate factorization, 
 
-\item CD (Content Dictionary) : assigns semantics to symbols
+{ox\_FGb} for Groebner basis computation (is it possible?) etc.
 
-\item Phrasebook : convesion between internal and OpenMath objects.
+$\Rightarrow$ Risa/Asir can be a front-end of efficient servers
 
-\item Encoding : format for actual data exchange
-\end{itemize}
+\item Trying to improve our implementation
 
-\item OpenXM
+Computation of $b$-function : still faster than any other system
+(Kan/sm1, Macaulay2) but not satisfactory
 
-\begin{itemize}
-\item Specification for encoding and exchanging messages
-
-\item It also specifies behavior of servers and session management
+$\Rightarrow$ Groebner basis computation in Weyl
+algebra should be improved
 \end{itemize}
 
-\end{itemize}
+\begin{center}
+\underline{In both cases, OpenXM interface is important}
+\end{center}
 \end{slide}
 
 \begin{slide}{}
@@ -374,14 +295,19 @@ The launcher launches a server on the same host.
 
 \item Server
 
-A server reads from the descriptor 3, write to the descriptor 4.
+Reads from the descriptor 3
 
+Writes to the descriptor 4
+
 \end{itemize}
 
 \item Subroutine call
 
-Risa/Asir subroutine library provides interfaces corresponding to
-pushing and popping data and executing stack commands.
+In Risa/Asir subroutine library {\tt libasir.a}:
+
+OpenXM functionalities are implemented as functon calls
+
+pushing and popping data, executing stack commands etc.
 \end{itemize}
 \end{slide}
 
@@ -395,14 +321,17 @@ Pushing and popping data, sending commands etc.
 
 \item Convenient functions
 
-Launching servers, calling remote functions,
- interrupting remote executions etc.
+Launching servers,
 
-\item Parallel distributed computation is easy
+Calling remote functions,
 
+Resetting remote executions etc.
+
+\item Parallel distributed computation
+
 Simple parallelization is practically important
 
-Competitive computation is easily realized 
+Competitive computation is easily realized ($\Rightarrow$ demo)
 \end{itemize}
 \end{slide}
 
@@ -461,39 +390,6 @@ 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}
@@ -792,6 +688,201 @@ The knapsack factorization is available via {\tt pari(
 \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 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{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 [Boehm]
+%
+%\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 [Traverso]
+%
+%\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 [SY]
+%\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 [NY]
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
+%
+%\begin{slide}{}
+%\fbox{History of development : 1996-1998}
+%
+%\begin{itemize}
+%\item Distributed compuatation
+%
+%\begin{itemize}
+%\item A prototype of OpenXM
+%\end{itemize}
+%
+%\item Improvement of Buchberger algorithm
+%
+%\begin{itemize}
+%\item Content reduction during nomal form computation
+%
+%\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
+%\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 [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 [Faug\`ere]
+%
+%\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 [Risa/Asir]
+%\end{itemize}
+%
+%\item OpenXM [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 [Takayama]
+%
+%\item $b$-function computation [Oaku]
+%
+%Minimal polynomial computation by modular method
+%\end{itemize}
+%\end{itemize}
+%
+%\end{slide}
 \begin{slide}{}
 \end{slide}