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version 1.6, 2000/01/15 02:24:18 version 1.7, 2000/01/15 03:23:59
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 % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.5 2000/01/11 05:35:48 noro Exp $  % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.6 2000/01/15 02:24:18 takayama Exp $
   
 \section{Design Outline}  \section{Design Outline}
   
Line 30  Although, data and control are orthogonal to each othe
Line 30  Although, data and control are orthogonal to each othe
 real world requires both.  real world requires both.
 NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},  NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
 and MathLink \cite{mathlink} provide both data and control integration.  and MathLink \cite{mathlink} provide both data and control integration.
 Each integration method has their own special features due to their  Each integration method has their own features due to their
 own design goals and design motivations.  own design goals and design motivations.
 OpenXM (Open message eXchange protocol for Mathematics)  OpenXM (Open message eXchange protocol for Mathematics)
 is a project aiming to integrate data, control and user interfaces  is a project aiming to integrate data, control and user interfaces
 with itw own set of design goals.  with its own set of design goals.
 To explain our design outline, we start with a list of  To explain our design outline, we start with a list of
 our motivations.  our motivations.
 \begin{enumerate}  \begin{enumerate}
 \item Noro has developed a general  \item Noro has developed a general
 purpose computer algebra system Risa/Asir \cite{asir}.  purpose computer algebra system Risa/Asir \cite{asir}.
 A set of functions for interactive distributed computations were introduced  An interface for interactive distributed computations was introduced
 in Risa/Asir version 950831 released in 1995.  in Risa/Asir version 950831 released in 1995.
 The model of computation was RPC (remote procedure call)  The model of computation was RPC (remote procedure call)
 and it had its own serialization method for objects.  and it had its own serialization.
 A robust interruption method was provided by having two communication channels  A robust interruption method was provided by having two communication channels
 like ftp.  like ftp.
 As an application of this robust and interactive distributed computation  As an application of this robust and the interactive distributed computation
 system, speed-up was achieved for a huge Gr\"obner basis computation  system, speed-up was achieved for a huge Gr\"obner basis computation
 to determine all odd order replicable functions  to determine all odd order replicable functions
 by Noro and McKay \cite{noro-mckay}.  by Noro and McKay \cite{noro-mckay}.
Line 54  However, the protocol was closed in Asir and we though
Line 54  However, the protocol was closed in Asir and we though
 design an open protocol.  design an open protocol.
 \item Takayama has developed  \item Takayama has developed
 a special purpose computer algebra system Kan/sm1 \cite{kan},  a special purpose computer algebra system Kan/sm1 \cite{kan},
 which is a Gr\"obner engine for the ring of differential operators $D$ and  which is a Gr\"obner engine for the ring of differential operators $D$.
 a package for computational algebraic geometry via D-module computations.  
 In order to implement algorithms in D-modules due to Oaku  In order to implement algorithms in D-modules due to Oaku
 (see, e.g., \cite{sst-book}),  (see, e.g., \cite{sst-book}),
 factorizations and primary ideal decompositions were necessary.  factorizations and primary ideal decompositions were necessary.
Line 69  for Risa/Asir to work as a server of factorization and
Line 68  for Risa/Asir to work as a server of factorization and
 decomposition.  decomposition.
 \item The number of mathematical softwares is increasing rapidly in the last  \item The number of mathematical softwares is increasing rapidly in the last
 decade of the 20th century.  decade of the 20th century.
 These are usually ``expert'' systems for one area of mathematics  These are usually ``expert'' systems in one area of mathematics
 such as ideals, groups, numbers, polytopes, and so on.  such as ideals, groups, numbers, polytopes, and so on.
 They have their own interfaces and data formats.  They have their own interfaces and data formats.
 Interfaces are usually specialized to a specific field of mathematics  Interfaces are sometimes specialized to a specific field of mathematics
 or poor because developers do not have time for designing user interface  or poor.
 languages.  
 It is fine for intensive and serious users of these systems.  It is fine for intensive and serious users of these systems.
 %% x2 stands for x^2, specialized for polynomial ring.  
 However, for users who want to explore a new area of mathematics with these  However, for users who want to explore a new area of mathematics with these
 softwares or users who need these systems only occasionally,  softwares or users who need these systems only occasionally,
 a unified system will be more convenient.  a unified system will be more convenient.
 For example, if we can call and use mathematical softwares  
 like CoCoa, GAP, Macaulay2, Porta, Singular, Snapea, $\ldots$  
 from Aldor, Asir, Axiom, Maple, Magma, muPAD, Mathematica, and so on,  
 it will be wonderful in research and education  
 of mathematics. This is an unification of user interfaces of mathematical  
 softwares.  
 \item  We believe that an open integrated system is a future of mathematical  \item  We believe that an open integrated system is a future of mathematical
 softwares.  softwares.
 However, it might be just a dream without realizability.  However, it might be just a dream without realizability.
Line 117  interface.
Line 109  interface.
 \item An output of the target must be understandable for computer programs;  \item An output of the target must be understandable for computer programs;
 it should follow a grammar that can be parsed with other softwares.  it should follow a grammar that can be parsed with other softwares.
 \end{enumerate}  \end{enumerate}
   \item Any server may have a hybrid interface;
   it may accept and execute its original command sequences.
   For example,
   if we send the following string to ox\_asir server
   {\footnotesize
   \begin{verbatim}
         " fctr(x^10-y^10); "
   \end{verbatim}
   }
   and call the stanck machine command
   SM\_executeStringByLocalParser,
   then the server executes the asir command
   \verb+ fctr(x^10-y^10); +
   (factorize $x^10-y^10$ over ${\bf Q}$)
   and push the result on the stack.
 \end{enumerate}  \end{enumerate}
 We are implementing a package, OpenXM package,  We are implementing a package, OpenXM package.
 which aims to realize our wishes stated as motivations.  
 It is based on above fundamental architecture.  It is based on above fundamental architecture.
 For example, the following is a command sequence to ask $1+1$ from  For example, the following is a command sequence to ask $1+1$ from
 the Asir client to the OX sm1 server:  the Asir client to the OX sm1 server:
Line 132  The current system, OpenXM on TCP/IP, 
Line 138  The current system, OpenXM on TCP/IP, 
 uses client-server model and the TCP/IP is used for interprocess  uses client-server model and the TCP/IP is used for interprocess
 communications.  communications.
 The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir  The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
 as we will see Section \ref{section:homog}.  as we will see in Section \ref{section:homog}.
 However, we focus only on the system based on TCP/IP in this paper.  However, we focus only on the system based on TCP/IP in this paper.
   
   
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