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1.9     ! takayama    1: % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.8 2000/01/15 03:47:58 takayama 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:
1.9     ! takayama   29: Although data and control are orthogonal to each other,
1.2       takayama   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.
1.7       takayama   33: Each integration method has their own features due to their
1.9     ! takayama   34: own design goals.
1.6       takayama   35: OpenXM (Open message eXchange protocol for Mathematics)
                     36: is a project aiming to integrate data, control and user interfaces
1.9     ! takayama   37: with design goals motivated by the followings.
1.2       takayama   38: \begin{enumerate}
1.9     ! takayama   39: \item Noro has involved in the development of a general
1.2       takayama   40: purpose computer algebra system Risa/Asir \cite{asir}.
1.7       takayama   41: An interface for interactive distributed computations was introduced
1.9     ! takayama   42: to Risa/Asir
        !            43: %% version 950831 released
        !            44: in 1995.
1.2       takayama   45: The model of computation was RPC (remote procedure call)
1.7       takayama   46: and it had its own serialization.
1.9     ! takayama   47: A robust interruption protocol was provided
        !            48: by  two communication channels
        !            49: like the File Transfer Protocol (ftp).
        !            50: As an application of this protocol,
        !            51: a parallel speed-up was achieved for a Gr\"obner basis computation
1.5       noro       52: to determine all odd order replicable functions
1.8       takayama   53: (Noro and McKay \cite{noro-mckay}).
1.9     ! takayama   54: However, the protocol was local in Asir and we thought that we should
1.2       takayama   55: design an open protocol.
1.6       takayama   56: \item Takayama has developed
1.9     ! takayama   57: a special purpose system Kan/sm1 \cite{kan},
1.7       takayama   58: which is a Gr\"obner engine for the ring of differential operators $D$.
1.9     ! takayama   59: In order to implement algorithms in $D$-modules due to Oaku
1.2       takayama   60: (see, e.g., \cite{sst-book}),
1.9     ! takayama   61: factorizations and primary ideal decompositions are necessary.
1.3       takayama   62: Kan/sm1 does not have an implementation for these and called
1.8       takayama   63: Risa/Asir as 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.
1.9     ! takayama   70: \item We have been profitted by increasing number
        !            71: of mathematical softwares.
1.7       takayama   72: These are usually ``expert'' systems in one area of mathematics
1.2       takayama   73: such as ideals, groups, numbers, polytopes, and so on.
1.3       takayama   74: They have their own interfaces and data formats.
1.9     ! takayama   75: It is fine for intensive users of these systems.
1.2       takayama   76: However, for users who want to explore a new area of mathematics with these
1.3       takayama   77: softwares or users who need these systems only occasionally,
1.4       ohara      78: a unified system will be more convenient.
1.7       takayama   79:
1.5       noro       80: \item  We believe that an open integrated system is a future of mathematical
1.2       takayama   81: softwares.
1.3       takayama   82: However, it might be just a dream without realizability.
1.9     ! takayama   83: We want to build a prototype of such an open system by using
1.2       takayama   84: existing standards, technologies and several mathematical softwares.
                     85: We want to see how far we can go with this approach.
                     86: \end{enumerate}
                     87:
                     88: Motivated with these, we started the OpenXM project with the following
                     89: fundamental architecture.
                     90: \begin{enumerate}
1.4       ohara      91: \item Communication is an exchange of messages. The messages are classified into
1.2       takayama   92: three types:
1.9     ! takayama   93: DATA, COMMAND, and SPECIAL.
        !            94: They are called OX (OpenXM) messages,
        !            95: {\it OX data messages} wrap mathematical data.
1.3       takayama   96: We use standards of mathematical data formats such as OpenMath and MP
1.9     ! takayama   97: as well as our own data format
        !            98: ({\it CMO --- Common Mathematical Object format}).
1.4       ohara      99: \item Servers, which provide services to other processes, are stack machines.
                    100: The stack machine is called the
                    101: {\it OX stack machine}.
                    102: Existing mathematical softwares are wrapped with this stack machine.
                    103: Minimal requirements for a target software wrapped with the OX stack machine
1.2       takayama  104: are as follows:
                    105: \begin{enumerate}
1.4       ohara     106: \item The target must have a serialized interface such as a character based
1.2       takayama  107: interface.
1.3       takayama  108: \item An output of the target must be understandable for computer programs;
1.4       ohara     109: it should follow a grammar that can be parsed with other softwares.
1.2       takayama  110: \end{enumerate}
1.7       takayama  111: \item Any server may have a hybrid interface;
                    112: it may accept and execute its original command sequences.
                    113: For example,
1.9     ! takayama  114: if we send the following string to {\tt ox\_asir} server
        !           115: (OpenXM server based on Risa/Asir) \\
        !           116: \verb+        " fctr(x^100-y^100); "      + \\
1.8       takayama  117: and call the stanck machine command  \\
1.9     ! takayama  118: \verb+        SM_executeStringByLocalParser    + \\
1.8       takayama  119: then the server executes the asir command \\
1.9     ! takayama  120: \verb+ fctr(x^100-y^100); +
        !           121: (factorize $x^{100}-y^{100}$ over ${\bf Q}$)
        !           122: and pushes the result onto the stack.
1.2       takayama  123: \end{enumerate}
1.8       takayama  124: OpenXM package  is based on above fundamental architecture.
1.2       takayama  125: For example, the following is a command sequence to ask $1+1$ from
1.9     ! takayama  126: the Asir client to the {\tt ox\_sm1} server:
1.2       takayama  127: \begin{verbatim}
                    128:   P = sm1_start();
                    129:   ox_push_cmo(P,1); ox_push_cmo(P,1);
                    130:   ox_execute_string(P,"add"); ox_pop_cmo(P);
                    131: \end{verbatim}
1.9     ! takayama  132: Here, {\tt ox\_sm1} is an OpenXM server based on Kan/sm1.
        !           133:
1.2       takayama  134: The current system, OpenXM on TCP/IP,
1.9     ! takayama  135: uses the client-server model.
1.6       takayama  136: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
1.7       takayama  137: as we will see in Section \ref{section:homog}.
1.3       takayama  138: However, we focus only on the system based on TCP/IP in this paper.
1.6       takayama  139:
1.2       takayama  140:
                    141:
1.1       takayama  142: