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 % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.1 1999/12/23 10:25:08 takayama 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 provides 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>
 \end{verbatim}  \end{verbatim}
 means the (OpenMath) integer $123$ in OpenMath, XML expression.  means the (OpenMath) integer $123$ in OpenMath/XML expression.
   
 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.  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
 infrastructure.  infrastructures.
 MCP (Mathematical Communication Protocol)  MCP (Mathematical Communication Protocol)
 by Wang \cite{iamc} is such a protocol specialized to mathematics.  by Wang \cite{iamc} is such a protocol specialized to mathematics.
   
 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.
 NetSolv \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 interative distributed computations were introduced  An interface for interactive distributed computations was introduced
 in Risa/Asir version 95xxxx release 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.
 One special feature of this system was that computations of remote servers can  
 be interrupted.  
 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 interractive system,  As an application of this robust and the interactive distributed computation
 a huge Gr\"obner basis was computed  system, speed-up was achieved for a huge Gr\"obner basis computation
 to determine all replicable functions by Noro and McKay \cite{noro-mckay}.  to determine all odd order replicable functions
 However, the protocol was closed in asir and we thought that we should  by Noro and McKay \cite{noro-mckay}.
   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 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.
 Kan/sm1 does not have an implementation for these and had invoked  Kan/sm1 does not have an implementation for these and called
 Risa/asir as a C library or a unix external program.  Risa/Asir as a C library or a UNIX external program.
 This approach was not satisfactory.  This approach was not satisfactory.
 Especially, we could not write a clean interface code between these  Especially, we could not write a clean interface code between these
 two systems.  two systems.
 We thought that it is necessary to provide a data and control protocol  We thought that it is necessary to provide a data and control protocol
 for Risa/asir to work as a server of factorization and primary ideal  for Risa/Asir to work as a server of factorization and primary ideal
 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
 decades of 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 has their own interfaces and data format.  They have their own interfaces and data formats.
 Interfaces are usually specialied to 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 needs these systems only occasionally,  softwares or users who need these systems only occasionally,
 a unified system will be more convinient.  a unified system will be more convenient.
 For example, if we can call and use mathematical softwares  
 like CoCoa, GAP, Macaulay2, Porta, Singular, Snapea, $\ldots$  \item  We believe that an open integrated system is a future of mathematical
 from Asir, Axion, 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.  softwares.
 \item  We believe that open integrated systems is a future of mathematical  However, it might be just a dream without realizability.
 softwares.  We want to build a prototype system of such an open system by using
 However, it might be just a dream without relizability.  
 We wanted to build a prototype system of such an open system by using  
 existing standards, technologies and several mathematical softwares.  existing standards, technologies and several mathematical softwares.
 We want to see how far we can go with this approach.  We want to see how far we can go with this approach.
 \end{enumerate}  \end{enumerate}
Line 98  We want to see how far we can go with this approach.
Line 89  We want to see how far we can go with this approach.
 Motivated with these, we started the OpenXM project with the following  Motivated with these, we started the OpenXM project with the following
 fundamental architecture.  fundamental architecture.
 \begin{enumerate}  \begin{enumerate}
 \item Communication is an exchange of messages. The messages are classifed into  \item Communication is an exchange of messages. The messages are classified into
 three types:  three types:
 DATA, COMMAND, and others.  DATA, COMMAND, and others.
 The messages are called OX (OpenXM) messages.  The messages are called OX (OpenXM) messages.
 Mathematical data are wrapped with OX messages.  Mathematical data are wrapped with {\it OX messages}.
 We uses standards of mathematical data formats such as OpenMath and MP  We use standards of mathematical data formats such as OpenMath and MP
 and our own data format (CMO --- Common Mathematical Object format)  and our own data format ({\it CMO --- Common Mathematical Object format})
 as data expressions.  as data expressions.
 \item Servers, which provide services to other processes, are stackmachines.  \item Servers, which provide services to other processes, are stack machines.
 The stackmachine is called the  The stack machine is called the
 OX stackmachine.  {\it OX stack machine}.
 Existing mathematical softwares are wrapped with this stackmachine.  Existing mathematical softwares are wrapped with this stack machine.
 Minimal requirements for a target software wrapped with OX stackmachine  Minimal requirements for a target software wrapped with the OX stack machine
 are as follows:  are as follows:
 \begin{enumerate}  \begin{enumerate}
 \item The target must have a seriealized interface such as a character based  \item The target must have a serialized interface such as a character based
 interface.  interface.
 \item An output of the target must be machine understandable.  \item An output of the target must be understandable for computer programs;
 It should follow a grammer 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 which is realizing our wishes stated as motivations.  We are implementing a package, OpenXM package.
 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:
 \begin{verbatim}  \begin{verbatim}
   P = sm1_start();    P = sm1_start();
   ox_push_cmo(P,1); ox_push_cmo(P,1);    ox_push_cmo(P,1); ox_push_cmo(P,1);
   ox_execute_string(P,"add"); ox_pop_cmo(P);    ox_execute_string(P,"add"); ox_pop_cmo(P);
 \end{verbatim}  \end{verbatim}
 The current system, OpenXM on TCP/IP,  The current system, OpenXM on TCP/IP,
 uses client-server model and the TCP/IP for interprocess  uses client-server model and the TCP/IP is used for interprocess
 communications.  communications.
 A design and implementation on MPI already exist for Risa/asir and  The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
 a OpenXM on MPI is a work in progress.  as we will see in Section \ref{section:homog}.
 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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