Annotation of OpenXM/doc/calc2000/design-outline.tex, Revision 1.6
1.6 ! noro 1: % $OpenXM: OpenXM/doc/calc2000/design-outline.tex,v 1.5 2000/04/26 08:18:30 noro 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
1.5 noro 10: programs or the same program.
1.1 noro 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
1.6 ! noro 32: platforms. Dalmas et al. \cite{omimp} shows an implementation of
! 33: OpenMath API, where Maple, REDUCE and
1.5 noro 34: AXIOM/Aldor are wrapped as servers. MP$+$MCP \cite{iamc} shows a design
1.6 ! noro 35: of server interface suited for interactive use and its limited
1.1 noro 36: implementation on MAXIMA is reported. Lakshman et al. \cite{pseware}
1.5 noro 37: proposes functionalities which a server should have and Maple is
1.6 ! noro 38: encapsulated as a server. These are all attempts to justify their
1.1 noro 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
1.5 noro 44: interactive use and efficient batch processing.
45: It includes various supports for developing programs on distributed
46: environment. We will show its
1.1 noro 47: usability by implementing and using it on various platforms.
48:
49: %NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc},
50: %and MathLink \cite{mathlink} provide both data and control integration.
51: %Each integration method has their own features determined by their
52: %own design goals.
53:
54: \section{Design Outline of OpenXM}
55:
56: OpenXM (Open message eXchange protocol for Mathematics)
57: is a project aiming to integrate data, control and user interfaces
1.6 ! noro 58: with design goals motivated by the following.
1.1 noro 59:
60: \begin{enumerate}
1.5 noro 61: \item
62: An interface for interactive distributed computations was introduced
1.6 ! noro 63: to Risa/Asir \cite{asir} in 1995.
1.5 noro 64: As an application,
65: a parallel speed-up was achieved for a Gr\"obner basis computation
66: (Noro and McKay \cite{noro-mckay}).
67: However, the protocol was local in Asir and we thought that we should
68: design an open protocol.
69: \item
70: In order to implement algorithms in $D$-modules due to Oaku
71: (see, e.g., \cite{sst-book}),
1.6 ! noro 72: Kan/sm1 \cite{kan} called Risa/Asir as a UNIX external program to
1.5 noro 73: compute factorizations and primary ideal decompositions,
74: but the interface code was not clean.
75: We thought that it is necessary to provide a data and control protocol
76: for Risa/Asir to work as a server.
77:
78: \item
79: There are increasing number of ``expert'' systems which are useful
80: but which have their own interfaces and data formats.
81: A unified system integrating such systems
82: will be more convenient
83: for users who want to explore a new area of mathematics with these
84: software tools or users who need these systems only occasionally.
85:
86: \item We believe that an open integrated system is a future of mathematical
87: software.
88: However, it might be just a dream without realizability.
89: We want to build a prototype of such an open system by using
90: existing standards, technologies and several mathematical software tools.
91: We want to see how far we can go with this approach.
92: \end{enumerate}
93:
94: Motivated with these, we started the OpenXM project with the following
95: fundamental architecture.
96: \begin{enumerate}
1.1 noro 97: \item Communication is an exchange of messages. The messages are classified into
98: three types:
99: DATA, COMMAND, and SPECIAL.
100: They are called OX (OpenXM) messages.
101: Among the three types,
102: {\it OX data messages} wrap mathematical data.
103: We use standards of mathematical data formats such as OpenMath and MP
104: as well as our own data format {\it CMO}
105: ({\it Common Mathematical Object format}).
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 tools are wrapped with this stack machine.
110: Minimal requirements for a target 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 tools.
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
1.6 ! noro 123: (OpenXM server based on Risa/Asir \\
1.1 noro 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.
1.5 noro 131: \item Network transparent supports for controlling servers are provided.
132: For example OpenXM defines a robust reset procedure to restart computations
133: without any confusion in I/O buffers.
1.6 ! noro 134: It is very useful for debugging programs running on distributed environment.
1.1 noro 135: \end{enumerate}
136: OpenXM package is implemented on above fundamental architecture.
137: Currently the following servers are available in the OpenXM package
138: \cite{openxm-web}.
139:
1.2 noro 140: \begin{description}
141: \item{\tt ox\_asir}
1.1 noro 142: A server for Risa/Asir, a general-purpose computer algebra
143: system. It provides almost
1.6 ! noro 144: all functionalities of Risa/Asir such as polynomial factorization,
1.1 noro 145: Gr\"obner basis computation and primary ideal decomposition.
1.2 noro 146: \item{\tt ox\_sm1}
1.6 ! noro 147: A server for Kan/sm1, a system for computation in
1.3 takayama 148: the ring of differential operators including computation of Gr\"obner bases
149: and cohomology groups.
150: \item {\tt ox\_phc}
1.1 noro 151: A server for PHC pack \cite{phc}, a general-purpose solver for
1.3 takayama 152: polynomial systems by homotopy continuation.
153: \item {\tt ox\_tigers}
1.1 noro 154: A server for TiGERS \cite{tigers}, a system to enumerate
155: all Gr\"obner bases of affine toric ideals.
156: It can be used to determine the state polytope
157: of a given affine toric ideal.
1.3 takayama 158: \item {\tt ox\_gnuplot}
1.1 noro 159: A server for GNUPLOT, a famous plotting tool.
160: \item {\tt ox\_math}
161: A server for Mathematica.
162: \item {\tt OMproxy}
163: A server for translation between CMO and OpenMath/XML expressions.
164: It is written in Java.
1.3 takayama 165: This module provides Java classes OXmessage, CMO, and SM
166: for the OpenXM protocol, too.
1.2 noro 167: \end{description}
1.1 noro 168: In addition to these servers, Risa/Asir, Kan/sm1 and Mathematica
169: can act as clients.
170: For example, the following is a command sequence to ask $1+1$ from
171: the Asir client to the {\tt ox\_sm1} server:
172: \begin{verbatim}
173: P = sm1_start();
174: ox_push_cmo(P,1); ox_push_cmo(P,1);
175: ox_execute_string(P,"add"); ox_pop_cmo(P);
176: \end{verbatim}
177: The OpenXM package is implemented on the OpenXM for TCP/IP,
178: which uses the client-server model.
179: The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir
180: as we will see in Section \ref{section:homog}.
181: In this paper, we discuss only on systems for TCP/IP
182: to concentrate on the core part of our design.
1.4 noro 183: Note that a C library interface is available for some servers.
1.1 noro 184:
185:
186:
187:
188:
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