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version 1.5, 2000/01/11 05:35:48 version 1.7, 2000/01/15 03:23:59
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 % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.4 2000/01/07 07:52:26 ohara 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 10  Data integration concerns with the exchange of data be
Line 10  Data integration concerns with the exchange of data be
 softwares or same softwares.  softwares or same softwares.
 OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,  OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
 for example, general purpose mathematical data protocols.  for example, general purpose mathematical data protocols.
 They provide a standard way to express mathematical objects.  They provide standard ways to express mathematical objects.
 For example,  For example,
 \begin{verbatim}  \begin{verbatim}
  <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>   <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
Line 19  means the (OpenMath) integer $123$ in OpenMath/XML exp
Line 19  means the (OpenMath) integer $123$ in OpenMath/XML exp
   
 Control integration concerns with the establishment and management of  Control integration concerns with the establishment and management of
 inter-software communications.  inter-software communications.
 Control involves, for example, a way to ask computation to other processes  Control involves, for example, a way to ask computations to other processes
 and a method to interrupt computations on servers from a client.  and a method to interrupt computations on servers from a client.
 RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or  RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
 infrastructures.  infrastructures.
Line 29  by Wang \cite{iamc} is such a protocol specialized to 
Line 29  by Wang \cite{iamc} is such a protocol specialized to 
 Although, data and control are orthogonal to each other,  Although, data and control are orthogonal to each other,
 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 of Mathematica provide both data and control integration.  and MathLink \cite{mathlink} provide both data and control integration.
 These are currently studied ways of data and control integration.  Each integration method has their own features due to their
 Each integration method has their own special features due to their  
 own design goals and design motivations.  own design goals and design motivations.
 OpenXM is a project aiming to integrate data, control and user interfaces  OpenXM (Open message eXchange protocol for Mathematics)
 from a different emphasis of a set of design goals with other projects.  is a project aiming to integrate data, control and user interfaces
   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,  who is one of the authors of OpenXM, 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, which implements the simple network management protocol.  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}.
 However, the protocol was closed in Asir and we thought that we should  However, the protocol was closed in Asir and we thought that we should
 design an open protocol.  design an open protocol.
 \item Takayama, who is also one of the authors of OpenXM, 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 Asir, Axiom, Maple, 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 131  the Asir client to the OX sm1 server:
Line 137  the Asir client to the OX sm1 server:
 The current system, OpenXM on TCP/IP,  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.
 A prototype OpenXM system on MPI \cite{MPI} already exists for Risa/Asir and  The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
 a general OpenXM on MPI is a work in progress.  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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