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1.4     ! noro        1: % $OpenXM: OpenXM/doc/calc2000/design-outline.tex,v 1.3 2000/04/24 06:38:27 takayama Exp $
1.1       noro        2:
                      3: \section{Integration of Mathematical Software}
                      4:
                      5: As Schefstr\"om clarified in \cite{schefstrom},
                      6: integration of software tools 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, real world
                     30: requires both. The best way to evaluate and to improve such
                     31: integration schemes is to implement and to use them on various
                     32: plaftforms.  Dalmas et al. \cite{omimp} shows an implementation of
                     33: OpenMath API, where several systems such as Maple, REDUCE and
                     34: AXIOM/Aldor are made as servers.  MP$+$MCP \cite{iamc} shows a design
                     35: of server inferface suited for interactive use and its limited
                     36: implementation on MAXIMA is reported.  Lakshman et al. \cite{pseware}
                     37: proposes functionalities which a server should have and Maple has been
                     38: encapsulated as a server. These are all attempts to justify thier
                     39: designs of protocols or architectures, but little is shown about their
                     40: practical usefulness, especially for developing real applications of
                     41: distributed computation.
                     42:
                     43: In this paper we propose a unified server interface fitting for both
                     44: interactive use and efficient batch processing. We hope to show its
                     45: usability by implementing and using it on various platforms.
                     46:
                     47: %NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
                     48: %and MathLink \cite{mathlink} provide both data and control integration.
                     49: %Each integration method has their own features determined by their
                     50: %own design goals.
                     51:
                     52: \section{Design Outline of OpenXM}
                     53:
                     54: %OpenXM (Open message eXchange protocol for Mathematics)
                     55: %is a project aiming to integrate data, control and user interfaces
                     56: %with design goals motivated by the followings.
                     57: %\begin{enumerate}
                     58: %\item Noro has been involved in the development of
                     59: %a computer algebra system Risa/Asir \cite{asir}.
                     60: %An interface for interactive distributed computations was introduced
                     61: %to Risa/Asir
                     62: %%% version 950831 released
                     63: %in 1995.
                     64: %The model of computation was RPC (remote procedure call).
                     65: %A robust interruption protocol was provided
                     66: %by  two communication channels
                     67: %like the File Transfer Protocol (ftp).
                     68: %As an application of this protocol,
                     69: %a parallel speed-up was achieved for a Gr\"obner basis computation
                     70: %to determine all odd order replicable functions
                     71: %(Noro and McKay \cite{noro-mckay}).
                     72: %However, the protocol was local in Asir and we thought that we should
                     73: %design an open protocol.
                     74: %\item Takayama has developed
                     75: %a special purpose system Kan/sm1 \cite{kan},
                     76: %which is a Gr\"obner engine for the ring of differential operators $D$.
                     77: %In order to implement algorithms in $D$-modules due to Oaku
                     78: %(see, e.g., \cite{sst-book}),
                     79: %factorizations and primary ideal decompositions are necessary.
                     80: %Kan/sm1 does not have an implementation for these and called
                     81: %Risa/Asir as a UNIX external program.
                     82: %This approach was not satisfactory.
                     83: %Especially, we could not write a clean interface code between these
                     84: %two systems.
                     85: %We thought that it is necessary to provide a data and control protocol
                     86: %for Risa/Asir to work as a server of factorization and primary ideal
                     87: %decomposition.
                     88: %\item We have been profited from increasing number
                     89: %of mathematical software tools.
                     90: %These are usually ``expert'' systems in one area of mathematics
                     91: %such as ideals, groups, numbers, polytopes, and so on.
                     92: %They have their own interfaces and data formats,
                     93: %which are fine for intensive users of these systems.
                     94: %However, a unified system will be more convenient
                     95: %for users who want to explore a new area of mathematics with these
                     96: %software tools or users who need these systems only occasionally.
                     97: %
                     98: %\item  We believe that an open integrated system is a future of mathematical
                     99: %software.
                    100: %However, it might be just a dream without realizability.
                    101: %We want to build a prototype of such an open system by using
                    102: %existing standards, technologies and several mathematical software tools.
                    103: %We want to see how far we can go with this approach.
                    104: %\end{enumerate}
                    105: %
                    106: %Motivated with these, we started the OpenXM project with the following
                    107: %fundamental architecture.
                    108: OpenXM (Open message eXchange protocol for Mathematics)
                    109: is a project aiming to integrate data, control and user interfaces
                    110: with the following design goals.
                    111:
                    112: \begin{enumerate}
                    113: \item Communication is an exchange of messages. The messages are classified into
                    114: three types:
                    115: DATA, COMMAND, and SPECIAL.
                    116: They are called OX (OpenXM) messages.
                    117: Among the three types,
                    118: {\it OX data messages} wrap mathematical data.
                    119: We use standards of mathematical data formats such as OpenMath and MP
                    120: as well as our own data format {\it CMO}
                    121: ({\it Common Mathematical Object format}).
                    122: \item Servers, which provide services to other processes, are stack machines.
                    123: The stack machine is called the
                    124: {\it OX stack machine}.
                    125: Existing mathematical software tools are wrapped with this stack machine.
                    126: Minimal requirements for a target wrapped with the OX stack machine
                    127: are as follows:
                    128: \begin{enumerate}
                    129: \item The target must have a serialized interface such as a character based
                    130: interface.
                    131: \item An output of the target must be understandable for computer programs;
                    132: it should follow a grammar that can be parsed with other software tools.
                    133: \end{enumerate}
                    134: \item Any server may have a hybrid interface;
                    135: it may accept and execute not only stack machine commands,
                    136: but also its original command sequences.
                    137: For example,
                    138: if we send the following string to the {\tt ox\_asir} server
                    139: (OpenXM server based on Risa/Asir \cite{asir}) \\
                    140: \verb+        " fctr(x^100-y^100); "      + \\
                    141: and call the stack machine command  \\
                    142: \verb+        SM_executeStringByLocalParser    + \\
                    143: then the server executes the asir command \\
                    144: \verb+ fctr(x^100-y^100); +
                    145: (factorize $x^{100}-y^{100}$ over ${\bf Q}$)
                    146: and pushes the result onto the stack.
                    147: \end{enumerate}
                    148: OpenXM package  is implemented on above fundamental architecture.
                    149: Currently the following servers are available in the OpenXM package
                    150: \cite{openxm-web}.
                    151:
1.2       noro      152: \begin{description}
                    153: \item{\tt ox\_asir}
1.1       noro      154: A server for Risa/Asir, a general-purpose computer algebra
                    155: system. It provides almost
                    156: all functinalities of Risa/Asir such as polynomial factorization,
                    157: Gr\"obner basis computation and primary ideal decomposition.
1.2       noro      158: \item{\tt ox\_sm1}
1.3       takayama  159: A server for Kan/sm1 \cite{kan}, a system for computation in
                    160: the ring of differential operators including computation of Gr\"obner bases
                    161: and cohomology groups.
                    162: \item {\tt ox\_phc}
1.1       noro      163: A server for PHC pack \cite{phc}, a general-purpose solver for
1.3       takayama  164: polynomial systems by homotopy continuation.
                    165: \item {\tt ox\_tigers}
1.1       noro      166: A server for TiGERS \cite{tigers}, a system to enumerate
                    167: all Gr\"obner bases of affine toric ideals.
                    168: It can be used to determine the state polytope
                    169: of a given affine toric ideal.
1.3       takayama  170: \item {\tt ox\_gnuplot}
1.1       noro      171: A server for GNUPLOT, a famous plotting tool.
                    172: \item {\tt ox\_math}
                    173: A server for Mathematica.
                    174: \item {\tt OMproxy}
                    175: A server for translation between CMO and OpenMath/XML expressions.
                    176: It is written in Java.
1.3       takayama  177: This module provides Java classes OXmessage, CMO, and SM
                    178: for the OpenXM protocol, too.
1.2       noro      179: \end{description}
1.1       noro      180: In addition to these servers, Risa/Asir, Kan/sm1 and Mathematica
                    181: can act as clients.
                    182: For example, the following is a command sequence to ask $1+1$ from
                    183: the Asir client to the {\tt ox\_sm1} server:
                    184: \begin{verbatim}
                    185:   P = sm1_start();
                    186:   ox_push_cmo(P,1); ox_push_cmo(P,1);
                    187:   ox_execute_string(P,"add"); ox_pop_cmo(P);
                    188: \end{verbatim}
                    189: The OpenXM package is implemented on the  OpenXM for TCP/IP,
                    190: which uses the client-server model.
                    191: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
                    192: as we will see in Section \ref{section:homog}.
                    193: In this paper, we discuss only on systems for TCP/IP
                    194: to concentrate on the core part of our design.
1.4     ! noro      195: Note that a C library interface is available for some servers.
1.1       noro      196:
                    197:
                    198:
                    199:
                    200:

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