Annotation of OpenXM/doc/calc2000/design-outline.tex, Revision 1.3
1.3 ! takayama 1: % $OpenXM: OpenXM/doc/calc2000/design-outline.tex,v 1.2 2000/04/24 05:01:29 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
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.
195:
196:
197:
198:
199:
200:
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