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1.1     ! noro        1: % $OpenXM$
        !             2:
        !             3: \section{Design Outline and OpenXM Request for Comments (OpenXM-RFC)}
        !             4:
        !             5: As Schefstr\"om clarified in \cite{schefstrom},
        !             6: integration of tools and software has three dimensions:
        !             7: data, control, and user interface.
        !             8:
        !             9: Data integration concerns with the exchange of data between different
        !            10: software or same software.
        !            11: OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are,
        !            12: for example, general purpose mathematical data protocols.
        !            13: They provide standard ways to express mathematical objects.
        !            14: For example,
        !            15: \begin{verbatim}
        !            16:  <OMOBJ>  <OMI> 123 </OMI> </OMOBJ>
        !            17: \end{verbatim}
        !            18: means the (OpenMath) integer $123$ in OpenMath/XML expression.
        !            19:
        !            20: Control integration concerns with the establishment and management of
        !            21: inter-software communications.
        !            22: Control involves, for example, a way to ask computations to other processes
        !            23: and a method to interrupt computations on servers from a client.
        !            24: RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or
        !            25: infrastructures.
        !            26: MCP (Mathematical Communication Protocol)
        !            27: by Wang \cite{iamc} is such a protocol for mathematics.
        !            28:
        !            29: Although data and control are orthogonal to each other,
        !            30: real world requires both.
        !            31: NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
        !            32: and MathLink \cite{mathlink} provide both data and control integration.
        !            33: Each integration method has their own features determined by their
        !            34: own design goals.
        !            35: OpenXM (Open message eXchange protocol for Mathematics)
        !            36: is a project aiming to integrate data, control and user interfaces
        !            37: with design goals motivated by the followings.
        !            38: \begin{enumerate}
        !            39: \item We should test the proposed standards mentioned above on
        !            40: various mathematical software systems, but the testing has not been
        !            41: enough.
        !            42: \item Noro has been involved in the development of
        !            43: a computer algebra system Risa/Asir \cite{asir}.
        !            44: An interface for interactive distributed computations was introduced
        !            45: to Risa/Asir
        !            46: %% version 950831 released
        !            47: in 1995.
        !            48: The model of computation was RPC (remote procedure call).
        !            49: A robust interruption protocol was provided
        !            50: by  two communication channels
        !            51: like the File Transfer Protocol (ftp).
        !            52: As an application of this protocol,
        !            53: a parallel speed-up was achieved for a Gr\"obner basis computation
        !            54: to determine all odd order replicable functions
        !            55: (Noro and McKay \cite{noro-mckay}).
        !            56: However, the protocol was local in Asir and we thought that we should
        !            57: design an open protocol.
        !            58: \item Takayama has developed
        !            59: a special purpose system Kan/sm1 \cite{kan},
        !            60: which is a Gr\"obner engine for the ring of differential operators $D$.
        !            61: In order to implement algorithms in $D$-modules due to Oaku
        !            62: (see, e.g., \cite{sst-book}),
        !            63: factorizations and primary ideal decompositions are necessary.
        !            64: Kan/sm1 does not have an implementation for these and called
        !            65: Risa/Asir as a UNIX external program.
        !            66: This approach was not satisfactory.
        !            67: Especially, we could not write a clean interface code between these
        !            68: two systems.
        !            69: We thought that it is necessary to provide a data and control protocol
        !            70: for Risa/Asir to work as a server of factorization and primary ideal
        !            71: decomposition.
        !            72: \item We have been profited from increasing number
        !            73: of mathematical software.
        !            74: These are usually ``expert'' systems in one area of mathematics
        !            75: such as ideals, groups, numbers, polytopes, and so on.
        !            76: They have their own interfaces and data formats,
        !            77: which are fine for intensive users of these systems.
        !            78: However, a unified system will be more convenient
        !            79: for users who want to explore a new area of mathematics with these
        !            80: software or users who need these systems only occasionally.
        !            81:
        !            82: \item  We believe that an open integrated system is a future of mathematical
        !            83: software.
        !            84: However, it might be just a dream without realizability.
        !            85: We want to build a prototype of such an open system by using
        !            86: existing standards, technologies and several mathematical software.
        !            87: We want to see how far we can go with this approach.
        !            88: \end{enumerate}
        !            89:
        !            90: Motivated with these, we started the OpenXM project with the following
        !            91: fundamental architecture, which is currently described in
        !            92: OpenXM-RFC 100  proposed standard %% ``draft standard'' and ``standard''
        !            93: ``Design and Implementation of OpenXM client-server model and common
        !            94: mathematical object format'' \cite{ox-rfc-100}.
        !            95: \begin{enumerate}
        !            96: \item Communication is an exchange of messages. The messages are classified into
        !            97: three types:
        !            98: DATA, COMMAND, and SPECIAL.
        !            99: They are called OX (OpenXM) messages.
        !           100: Among the three types,
        !           101: {\it OX data messages} wrap mathematical data.
        !           102: We use standards of mathematical data formats such as OpenMath and MP
        !           103: as well as our own data format {\it CMO}
        !           104: ({\it Common Mathematical Object format}),
        !           105: which can be expressed in terms of XML.
        !           106: \item Servers, which provide services to other processes, are stack machines.
        !           107: The stack machine is called the
        !           108: {\it OX stack machine}.
        !           109: Existing mathematical software systems are wrapped with this stack machine.
        !           110: Minimal requirements for a target software wrapped with the OX stack machine
        !           111: are as follows:
        !           112: \begin{enumerate}
        !           113: \item The target must have a serialized interface such as a character based
        !           114: interface.
        !           115: \item An output of the target must be understandable for computer programs;
        !           116: it should follow a grammar that can be parsed with other software.
        !           117: \end{enumerate}
        !           118: \item Any server may have a hybrid interface;
        !           119: it may accept and execute not only stack machine commands,
        !           120: but also its original command sequences.
        !           121: For example,
        !           122: if we send the following string to the {\tt ox\_asir} server
        !           123: (OpenXM server of Risa/Asir) \\
        !           124: \verb+        " fctr(x^100-y^100); "      + \\
        !           125: and call the stack machine command  \\
        !           126: \verb+        SM_executeStringByLocalParser    + \\
        !           127: then the server executes the asir command \\
        !           128: \verb+ fctr(x^100-y^100); +
        !           129: (factorize $x^{100}-y^{100}$ over ${\bf Q}$)
        !           130: and pushes the result onto the stack.
        !           131: \end{enumerate}
        !           132: OpenXM package  implements the OpenXM-RFC 100 \cite{ox-rfc-100}
        !           133: and 101 \cite{ox-rfc-101} based on
        !           134: the above fundamental architecture.
        !           135: In this paper, we discuss mainly on systems implementing
        !           136: OpenXM-RFC 100 and 101 on TCP/IP.
        !           137: For example, the following is a command sequence to ask $1+1$ from
        !           138: the Asir client to the {\tt ox\_sm1} server through TCP/IP:
        !           139: \begin{verbatim}
        !           140:   P = sm1_start();
        !           141:   ox_push_cmo(P,1); ox_push_cmo(P,1);
        !           142:   ox_execute_string(P,"add"); ox_pop_cmo(P);
        !           143: \end{verbatim}
        !           144: Here, {\tt ox\_sm1} is an OpenXM server of Kan/sm1.
        !           145:
        !           146: Our project of integrating mathematical software
        !           147: systems is taking the ``RFC'' approach, which has been
        !           148: used to develop internet protocols.
        !           149: We think that ``RFC'' approach is an excellent way and
        !           150: we hope that other groups, who are working on standard protocols,
        !           151: take this ``RFC'' approach, too.
        !           152:
        !           153: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
        !           154: as we will see in Section \ref{section:homog}.
        !           155: We are now preparing the OpenXM-RFC 102 ``Mathematical communication
        !           156: on MPI'' (draft protocol)
        !           157: based on our experiments on MPI.
        !           158:
        !           159: In the rest of the paper, we abbreviate
        !           160: OpenXM-RFC 100 and 101 to OpenXM if no confusion arises.
        !           161:
        !           162:
        !           163:
        !           164:
        !           165:
        !           166:
        !           167:
        !           168:
        !           169: