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1.6     ! takayama    1: % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.5 2000/01/11 05:35:48 noro Exp $
1.2       takayama    2:
                      3: \section{Design Outline}
                      4:
                      5: As Schefstr\"om clarified in \cite{schefstrom},
                      6: integration of tools and softwares has three dimensions:
                      7: data, control, and user interface.
                      8:
                      9: Data integration concerns with the exchange of data between different
                     10: softwares or same softwares.
                     11: OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
                     12: for example, general purpose mathematical data protocols.
1.6     ! takayama   13: They provide standard ways to express mathematical objects.
1.2       takayama   14: For example,
                     15: \begin{verbatim}
                     16:  <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
                     17: \end{verbatim}
1.3       takayama   18: means the (OpenMath) integer $123$ in OpenMath/XML expression.
1.2       takayama   19:
                     20: Control integration concerns with the establishment and management of
1.3       takayama   21: inter-software communications.
1.6     ! takayama   22: Control involves, for example, a way to ask computations to other processes
1.3       takayama   23: and a method to interrupt computations on servers from a client.
1.2       takayama   24: RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
1.3       takayama   25: infrastructures.
1.2       takayama   26: MCP (Mathematical Communication Protocol)
                     27: by Wang \cite{iamc} is such a protocol specialized to mathematics.
                     28:
                     29: Although, data and control are orthogonal to each other,
                     30: real world requires both.
1.4       ohara      31: NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
1.6     ! takayama   32: and MathLink \cite{mathlink} provide both data and control integration.
1.2       takayama   33: Each integration method has their own special features due to their
                     34: own design goals and design motivations.
1.6     ! takayama   35: OpenXM (Open message eXchange protocol for Mathematics)
        !            36: is a project aiming to integrate data, control and user interfaces
        !            37: with itw own set of design goals.
1.2       takayama   38: To explain our design outline, we start with a list of
                     39: our motivations.
                     40: \begin{enumerate}
1.6     ! takayama   41: \item Noro has developed a general
1.2       takayama   42: purpose computer algebra system Risa/Asir \cite{asir}.
1.4       ohara      43: A set of functions for interactive distributed computations were introduced
1.3       takayama   44: in Risa/Asir version 950831 released in 1995.
1.2       takayama   45: The model of computation was RPC (remote procedure call)
                     46: and it had its own serialization method for objects.
                     47: A robust interruption method was provided by having two communication channels
1.6     ! takayama   48: like ftp.
1.4       ohara      49: As an application of this robust and interactive distributed computation
1.5       noro       50: system, speed-up was achieved for a huge Gr\"obner basis computation
                     51: to determine all odd order replicable functions
                     52: by Noro and McKay \cite{noro-mckay}.
                     53: However, the protocol was closed in Asir and we thought that we should
1.2       takayama   54: design an open protocol.
1.6     ! takayama   55: \item Takayama has developed
1.2       takayama   56: a special purpose computer algebra system Kan/sm1 \cite{kan},
1.3       takayama   57: which is a Gr\"obner engine for the ring of differential operators $D$ and
1.2       takayama   58: a package for computational algebraic geometry via D-module computations.
                     59: In order to implement algorithms in D-modules due to Oaku
                     60: (see, e.g., \cite{sst-book}),
                     61: factorizations and primary ideal decompositions were necessary.
1.3       takayama   62: Kan/sm1 does not have an implementation for these and called
1.5       noro       63: Risa/Asir as a C library or a UNIX external program.
1.2       takayama   64: This approach was not satisfactory.
                     65: Especially, we could not write a clean interface code between these
                     66: two systems.
                     67: We thought that it is necessary to provide a data and control protocol
1.5       noro       68: for Risa/Asir to work as a server of factorization and primary ideal
1.2       takayama   69: decomposition.
                     70: \item The number of mathematical softwares is increasing rapidly in the last
1.3       takayama   71: decade of the 20th century.
1.2       takayama   72: These are usually ``expert'' systems for one area of mathematics
                     73: such as ideals, groups, numbers, polytopes, and so on.
1.3       takayama   74: They have their own interfaces and data formats.
1.4       ohara      75: Interfaces are usually specialized to a specific field of mathematics
1.2       takayama   76: or poor because developers do not have time for designing user interface
                     77: languages.
                     78: It is fine for intensive and serious users of these systems.
                     79: %% x2 stands for x^2, specialized for polynomial ring.
                     80: However, for users who want to explore a new area of mathematics with these
1.3       takayama   81: softwares or users who need these systems only occasionally,
1.4       ohara      82: a unified system will be more convenient.
1.2       takayama   83: For example, if we can call and use mathematical softwares
                     84: like CoCoa, GAP, Macaulay2, Porta, Singular, Snapea, $\ldots$
1.6     ! takayama   85: from Aldor, Asir, Axiom, Maple, Magma, muPAD, Mathematica, and so on,
1.2       takayama   86: it will be wonderful in research and education
                     87: of mathematics. This is an unification of user interfaces of mathematical
                     88: softwares.
1.5       noro       89: \item  We believe that an open integrated system is a future of mathematical
1.2       takayama   90: softwares.
1.3       takayama   91: However, it might be just a dream without realizability.
1.5       noro       92: We want to build a prototype system of such an open system by using
1.2       takayama   93: existing standards, technologies and several mathematical softwares.
                     94: We want to see how far we can go with this approach.
                     95: \end{enumerate}
                     96:
                     97: Motivated with these, we started the OpenXM project with the following
                     98: fundamental architecture.
                     99: \begin{enumerate}
1.4       ohara     100: \item Communication is an exchange of messages. The messages are classified into
1.2       takayama  101: three types:
                    102: DATA, COMMAND, and others.
                    103: The messages are called OX (OpenXM) messages.
1.3       takayama  104: Mathematical data are wrapped with {\it OX messages}.
                    105: We use standards of mathematical data formats such as OpenMath and MP
                    106: and our own data format ({\it CMO --- Common Mathematical Object format})
1.2       takayama  107: as data expressions.
1.4       ohara     108: \item Servers, which provide services to other processes, are stack machines.
                    109: The stack machine is called the
                    110: {\it OX stack machine}.
                    111: Existing mathematical softwares are wrapped with this stack machine.
                    112: Minimal requirements for a target software wrapped with the OX stack machine
1.2       takayama  113: are as follows:
                    114: \begin{enumerate}
1.4       ohara     115: \item The target must have a serialized interface such as a character based
1.2       takayama  116: interface.
1.3       takayama  117: \item An output of the target must be understandable for computer programs;
1.4       ohara     118: it should follow a grammar that can be parsed with other softwares.
1.2       takayama  119: \end{enumerate}
                    120: \end{enumerate}
1.3       takayama  121: We are implementing a package, OpenXM package,
                    122: which aims to realize our wishes stated as motivations.
1.2       takayama  123: It is based on above fundamental architecture.
                    124: For example, the following is a command sequence to ask $1+1$ from
1.5       noro      125: the Asir client to the OX sm1 server:
1.2       takayama  126: \begin{verbatim}
                    127:   P = sm1_start();
                    128:   ox_push_cmo(P,1); ox_push_cmo(P,1);
                    129:   ox_execute_string(P,"add"); ox_pop_cmo(P);
                    130: \end{verbatim}
                    131: The current system, OpenXM on TCP/IP,
1.3       takayama  132: uses client-server model and the TCP/IP is used for interprocess
1.2       takayama  133: communications.
1.6     ! takayama  134: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
        !           135: as we will see Section \ref{section:homog}.
1.3       takayama  136: However, we focus only on the system based on TCP/IP in this paper.
1.6     ! takayama  137:
1.2       takayama  138:
                    139:
1.1       takayama  140: