Annotation of OpenXM/doc/calc2000/design-outline.tex, Revision 1.1
1.1 ! noro 1: % $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.13 2000/01/17 08:06:15 noro Exp $
! 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:
! 152: \begin{itemize}
! 153: \item {\tt ox\_asir}
! 154:
! 155: A server for Risa/Asir, a general-purpose computer algebra
! 156: system. It provides almost
! 157: all functinalities of Risa/Asir such as polynomial factorization,
! 158: Gr\"obner basis computation and primary ideal decomposition.
! 159: \item {\tt ox\_sm1}
! 160:
! 161: A server for Kan/sm1 \cite{kan}, a system for computation in algebraic
! 162: analysis.
! 163:
! 164: \item {\tt ox\_sm1\_phc}
! 165:
! 166: A server for PHC pack \cite{phc}, a general-purpose solver for
! 167: polynomial systems by homotopy continuation. It is available only
! 168: on Linux.
! 169:
! 170: \item {\tt ox\_sm1\_tigers}
! 171:
! 172: A server for TiGERS \cite{tigers}, a system to enumerate
! 173: all Gr\"obner bases of affine toric ideals.
! 174: It can be used to determine the state polytope
! 175: of a given affine toric ideal.
! 176:
! 177: \item {\tt ox\_sm1\_gnuplot}
! 178:
! 179: A server for GNUPLOT, a famous plotting tool.
! 180: \item {\tt ox\_math}
! 181:
! 182: A server for Mathematica.
! 183:
! 184: \item {\tt OMproxy}
! 185:
! 186: A server for translation between CMO and OpenMath/XML expressions.
! 187: It is written in Java.
! 188: \end{itemize}
! 189: In addition to these servers, Risa/Asir, Kan/sm1 and Mathematica
! 190: can act as clients.
! 191: For example, the following is a command sequence to ask $1+1$ from
! 192: the Asir client to the {\tt ox\_sm1} server:
! 193: \begin{verbatim}
! 194: P = sm1_start();
! 195: ox_push_cmo(P,1); ox_push_cmo(P,1);
! 196: ox_execute_string(P,"add"); ox_pop_cmo(P);
! 197: \end{verbatim}
! 198: The OpenXM package is implemented on the OpenXM for TCP/IP,
! 199: which uses the client-server model.
! 200: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
! 201: as we will see in Section \ref{section:homog}.
! 202: In this paper, we discuss only on systems for TCP/IP
! 203: to concentrate on the core part of our design.
! 204:
! 205:
! 206:
! 207:
! 208:
! 209:
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