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1.2     ! takayama    1: % $OpenXM: OpenXM/doc/ascm2001p/design-outline.tex,v 1.1 2001/06/19 07:32:58 noro Exp $
1.1       noro        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)
1.2     ! takayama   27: by Wang \cite{iamc} and OMEI \cite{omei} are such protocols for mathematics.
1.1       noro       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.
1.2     ! takayama   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.
1.1       noro       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:

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