=================================================================== RCS file: /home/cvs/OpenXM/doc/issac2000/design-outline.tex,v retrieving revision 1.5 retrieving revision 1.12 diff -u -p -r1.5 -r1.12 --- OpenXM/doc/issac2000/design-outline.tex 2000/01/11 05:35:48 1.5 +++ OpenXM/doc/issac2000/design-outline.tex 2000/01/16 10:55:40 1.12 @@ -1,4 +1,4 @@ -% $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.4 2000/01/07 07:52:26 ohara Exp $ +% $OpenXM: OpenXM/doc/issac2000/design-outline.tex,v 1.11 2000/01/16 06:02:41 takayama Exp $ \section{Design Outline} @@ -10,7 +10,7 @@ Data integration concerns with the exchange of data be softwares or same softwares. OpenMath \cite{OpenMath} and MP (Multi Protocol) \cite{GKW} are, for example, general purpose mathematical data protocols. -They provide a standard way to express mathematical objects. +They provide standard ways to express mathematical objects. For example, \begin{verbatim} 123 @@ -19,77 +19,67 @@ means the (OpenMath) integer $123$ in OpenMath/XML exp Control integration concerns with the establishment and management of inter-software communications. -Control involves, for example, a way to ask computation to other processes +Control involves, for example, a way to ask computations to other processes and a method to interrupt computations on servers from a client. RPC, HTTP, MPI, PVM are regarded as a general purpose control protocols or infrastructures. MCP (Mathematical Communication Protocol) -by Wang \cite{iamc} is such a protocol specialized to mathematics. +by Wang \cite{iamc} is such a protocol for mathematics. -Although, data and control are orthogonal to each other, +Although data and control are orthogonal to each other, real world requires both. NetSolve \cite{netsolve}, OpenMath$+$MCP, MP$+$MCP \cite{iamc}, -and MathLink of Mathematica provide both data and control integration. -These are currently studied ways of data and control integration. -Each integration method has their own special features due to their -own design goals and design motivations. -OpenXM is a project aiming to integrate data, control and user interfaces -from a different emphasis of a set of design goals with other projects. -To explain our design outline, we start with a list of -our motivations. +and MathLink \cite{mathlink} provide both data and control integration. +Each integration method has their own features determined by their +own design goals. +OpenXM (Open message eXchange protocol for Mathematics) +is a project aiming to integrate data, control and user interfaces +with design goals motivated by the followings. \begin{enumerate} -\item Noro, who is one of the authors of OpenXM, has developed a general -purpose computer algebra system Risa/Asir \cite{asir}. -A set of functions for interactive distributed computations were introduced -in Risa/Asir version 950831 released in 1995. -The model of computation was RPC (remote procedure call) -and it had its own serialization method for objects. -A robust interruption method was provided by having two communication channels -like ftp, which implements the simple network management protocol. -As an application of this robust and interactive distributed computation -system, speed-up was achieved for a huge Gr\"obner basis computation +\item Noro has been involved in the development of +a computer algebra system Risa/Asir \cite{asir}. +An interface for interactive distributed computations was introduced +to Risa/Asir +%% version 950831 released +in 1995. +The model of computation was RPC (remote procedure call). +A robust interruption protocol was provided +by two communication channels +like the File Transfer Protocol (ftp). +As an application of this protocol, +a parallel speed-up was achieved for a Gr\"obner basis computation to determine all odd order replicable functions -by Noro and McKay \cite{noro-mckay}. -However, the protocol was closed in Asir and we thought that we should +(Noro and McKay \cite{noro-mckay}). +However, the protocol was local in Asir and we thought that we should design an open protocol. -\item Takayama, who is also one of the authors of OpenXM, has developed -a special purpose computer algebra system Kan/sm1 \cite{kan}, -which is a Gr\"obner engine for the ring of differential operators $D$ and -a package for computational algebraic geometry via D-module computations. -In order to implement algorithms in D-modules due to Oaku +\item Takayama has developed +a special purpose system Kan/sm1 \cite{kan}, +which is a Gr\"obner engine for the ring of differential operators $D$. +In order to implement algorithms in $D$-modules due to Oaku (see, e.g., \cite{sst-book}), -factorizations and primary ideal decompositions were necessary. +factorizations and primary ideal decompositions are necessary. Kan/sm1 does not have an implementation for these and called -Risa/Asir as a C library or a UNIX external program. +Risa/Asir as a UNIX external program. This approach was not satisfactory. Especially, we could not write a clean interface code between these two systems. We thought that it is necessary to provide a data and control protocol for Risa/Asir to work as a server of factorization and primary ideal decomposition. -\item The number of mathematical softwares is increasing rapidly in the last -decade of the 20th century. -These are usually ``expert'' systems for one area of mathematics +\item We have been profitted from increasing number +of mathematical softwares. +These are usually ``expert'' systems in one area of mathematics such as ideals, groups, numbers, polytopes, and so on. -They have their own interfaces and data formats. -Interfaces are usually specialized to a specific field of mathematics -or poor because developers do not have time for designing user interface -languages. -It is fine for intensive and serious users of these systems. -%% x2 stands for x^2, specialized for polynomial ring. -However, for users who want to explore a new area of mathematics with these -softwares or users who need these systems only occasionally, -a unified system will be more convenient. -For example, if we can call and use mathematical softwares -like CoCoa, GAP, Macaulay2, Porta, Singular, Snapea, $\ldots$ -from Asir, Axiom, Maple, muPAD, Mathematica, and so on, -it will be wonderful in research and education -of mathematics. This is an unification of user interfaces of mathematical -softwares. +They have their own interfaces and data formats, +which are fine for intensive users of these systems. +However, a unified system will be more convenient +for users who want to explore a new area of mathematics with these +softwares or users who need these systems only occasionally. + \item We believe that an open integrated system is a future of mathematical softwares. However, it might be just a dream without realizability. -We want to build a prototype system of such an open system by using +We want to build a prototype of such an open system by using existing standards, technologies and several mathematical softwares. We want to see how far we can go with this approach. \end{enumerate} @@ -99,12 +89,13 @@ fundamental architecture. \begin{enumerate} \item Communication is an exchange of messages. The messages are classified into three types: -DATA, COMMAND, and others. -The messages are called OX (OpenXM) messages. -Mathematical data are wrapped with {\it OX messages}. +DATA, COMMAND, and SPECIAL. +They are called OX (OpenXM) messages. +Among the three types, +{\it OX data messages} wrap mathematical data. We use standards of mathematical data formats such as OpenMath and MP -and our own data format ({\it CMO --- Common Mathematical Object format}) -as data expressions. +as well as our own data format {\it CMO} +({\it Common Mathematical Object format}). \item Servers, which provide services to other processes, are stack machines. The stack machine is called the {\it OX stack machine}. @@ -117,23 +108,39 @@ interface. \item An output of the target must be understandable for computer programs; it should follow a grammar that can be parsed with other softwares. \end{enumerate} +\item Any server may have a hybrid interface; +it may accept and execute not only stack machine commands, +but also its original command sequences. +For example, +if we send the following string to the {\tt ox\_asir} server +(OpenXM server based on Risa/Asir) \\ +\verb+ " fctr(x^100-y^100); " + \\ +and call the stanck machine command \\ +\verb+ SM_executeStringByLocalParser + \\ +then the server executes the asir command \\ +\verb+ fctr(x^100-y^100); + +(factorize $x^{100}-y^{100}$ over ${\bf Q}$) +and pushes the result onto the stack. \end{enumerate} -We are implementing a package, OpenXM package, -which aims to realize our wishes stated as motivations. -It is based on above fundamental architecture. +OpenXM package is implemented on above fundamental architecture. For example, the following is a command sequence to ask $1+1$ from -the Asir client to the OX sm1 server: +the Asir client to the {\tt ox\_sm1} server: \begin{verbatim} P = sm1_start(); ox_push_cmo(P,1); ox_push_cmo(P,1); ox_execute_string(P,"add"); ox_pop_cmo(P); \end{verbatim} -The current system, OpenXM on TCP/IP, -uses client-server model and the TCP/IP is used for interprocess -communications. -A prototype OpenXM system on MPI \cite{MPI} already exists for Risa/Asir and -a general OpenXM on MPI is a work in progress. -However, we focus only on the system based on TCP/IP in this paper. +Here, {\tt ox\_sm1} is an OpenXM server based on Kan/sm1. + +The OpenXM package is implemented on the OpenXM for TCP/IP, +which uses the client-server model. +The OpenXM on MPI \cite{MPI} is currently running on Risa/Asir +as we will see in Section \ref{section:homog}. +In this paper, we discuss only on systems for TCP/IP +to concentrate on the core part of our design. + + +