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version 1.2, 2000/01/02 07:32:11 version 1.5, 2000/01/13 10:58:16
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 % $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.1 1999/12/23 10:25:08 takayama Exp $  % $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.4 2000/01/11 05:35:48 noro Exp $
   
 \section{Data Format}   (Ohara)  \section{Data Format}   (Ohara)
   
 OpenXM admits multiple math encodings such as OpenMath, MP, CMO  OpenXM admits multiple mathematical encodings such as OpenMath, MP, CMO
 (Common Mathematical Object format).  (Common Mathematical Object format).
 OpenXM itself does not exhibit a bias towards a particular encodings  OpenXM itself does not exhibit a bias towards a particular encodings
 as a main math data carrier and OpenXM compliant system do not need to  as a main mathematical data carrier and an OpenXM compliant system do not need to
 implement all possible data formats.  implement all possible data formats.
 A server or a client does not necessarily implement full specifications  A server or a client does not necessarily implement full specifications
 of OpenXM.  of OpenXM.
Line 13  However, if a program sends an OX data or an OX comman
Line 13  However, if a program sends an OX data or an OX comman
 an unrecoverable error may occur.  an unrecoverable error may occur.
 To avoid such a case OpenXM provides a scheme not  To avoid such a case OpenXM provides a scheme not
 to send an OX message unknown to peers.  to send an OX message unknown to peers.
 It is realized by exchanging the list of  It is realized by exchanging a list of
 supported CMO's, OpenXM stack machine codes, and necessary extra informations.  supported CMO's, OpenXM stack machine codes, and necessary extra informations.
 The list is called mathcap.  The list is called {\it mathcap}.
 Mathcap is also defined as a CMO and the elements are 32bit integers  % Mathcap is also defined as a CMO and its elements are 32bit integers
 or strings.  % or strings.
   Mathcap is also defined as a CMO and the CMO has a structure of a nest
   of lists.  its leafs of the end are also a CMO which tags with
   CMO\_INT32 or CMO\_STRING.
   
 Math encoding types of OX data are distinguished with tags  Mathematical encoding types of OX data are distinguished with tags
 of OX messages.  of OX messages.
 For example,  For example,
 an OX message with the tag  an OX message with the tag
 OX\_DATA is followed by CMO packet.  OX\_DATA is followed by a CMO packet.
 An OX message with the tag  An OX message with the tag
 OX\_DATA\_OPENMATH\_XML is followed by  OX\_DATA\_OPENMATH\_XML is followed by
 OpenMath XML string and its length.  an OpenMath XML string and its length.
 All OpenXM compliant systems should implement 7 primitive data types  
 of CMO.  All OpenXM compliant systems should implement seven primitive data types
   of the CMO.
 These are used not only to express mathematical objects, but also  These are used not only to express mathematical objects, but also
 indespensable to carry control informations such as mathcap.  indispensable to carry control informations such as mathcap.
 CMO is an original methematical data encoding system of the OpenXM project.  CMO is an original mathematical data encoding system of the OpenXM project.
 Let us explain the data format of CMO.  Let us explain the data format of CMO.
 Any CMO packet consists of a header and a body.  Any CMO packet consists of a header and a body.
 The size of the header is 4 bytes that tags the data type of the body.  The size of the header is 4 bytes that tags the data type of the body.
Line 46  Following tags are registered in the OpenXM for now.
Line 50  Following tags are registered in the OpenXM for now.
 #define CMO_STRING                         4  #define CMO_STRING                         4
 #define CMO_MATHCAP                        5  #define CMO_MATHCAP                        5
 #define CMO_LIST                           17  #define CMO_LIST                           17
   
 #define CMO_MONOMIAL32                     19  #define CMO_MONOMIAL32                     19
 #define CMO_ZZ                             20  #define CMO_ZZ                             20
 #define CMO_QQ                             21  #define CMO_QQ                             21
Line 70  Following tags are registered in the OpenXM for now.
Line 75  Following tags are registered in the OpenXM for now.
 #define CMO_LAMBDA                         62  #define CMO_LAMBDA                         62
 \end{verbatim}  \end{verbatim}
 The first seven types should be implemented on all OpenXM compliant systems.  The first seven types should be implemented on all OpenXM compliant systems.
 The format of the first severn CMO's are as follows. \\  The format of the first seven CMO's are as follows. \\
 \begin{tabular}{|c|c|}  \begin{tabular}{|c|c|}
 \hline  \hline
 {\tt int32 CMO\_ERROR2} & {\sl CMObject} {\rm ob} \\  {\sl int32} {\tt CMO\_ERROR2} & {\sl CMObject} {\rm ob} \\
 \hline  \hline
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|}  \begin{tabular}{|c|c|}
 \hline  \hline
 {\tt int32 CMO\_NULL}  \\  {\sl int32} {\tt CMO\_NULL}  \\
 \hline  \hline
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|}  \begin{tabular}{|c|c|}
 \hline  \hline
 {\tt int32 CMO\_INT32}& {\tt int32} {\rm n}  \\  {\sl int32} {\tt CMO\_INT32}& {\sl int32} {\rm n}  \\
 \hline  \hline
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|c|}  \begin{tabular}{|c|c|c|}
 \hline  \hline
 {\tt int32 CMO\_DATUM}& {\tt int32} {\rm n} & {\tt byte} {\rm  data[0]} \\  {\sl int32} {\tt CMO\_DATUM}& {\sl int32} {\rm n} & {\sl byte} {\rm  data[0]} \\
 \hline  \hline
 $\cdots$ & {\tt byte} {\rm  data[n-1]} \\  $\cdots$ & {\sl byte} {\rm  data[n-1]} \\
 \cline{1-2}  \cline{1-2}
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|c|}  \begin{tabular}{|c|c|c|}
 \hline  \hline
 {\tt int32 CMO\_STRING}& {\tt int32} {\rm n} & {\tt byte} {\rm data[0]} \\  {\sl int32} {\tt CMO\_STRING}& {\sl int32} {\rm n} & {\sl byte} {\rm data[0]} \\
 \hline  \hline
 $\cdots$ & {\tt byte} {\rm data[n-1]} \\  $\cdots$ & {\sl byte} {\rm data[n-1]} \\
 \cline{1-2}  \cline{1-2}
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|}  \begin{tabular}{|c|c|}
 \hline  \hline
 {\tt int32 CMO\_MATHCAP} & {\it CMObject} {\rm ob} \\  {\sl int32} {\tt CMO\_MATHCAP} & {\sl CMObject} {\rm ob} \\
 \hline  \hline
 \end{tabular} \\  \end{tabular} \\
 \begin{tabular}{|c|c|c|}  \begin{tabular}{|c|c|c|}
 \hline  \hline
 {\tt int32 CMO\_LIST}& {\tt int32} {\rm n} & {\tt CMObject} {\rm ob[0]} \\  {\sl int32} {\tt CMO\_LIST}& {\sl int32} {\rm n} & {\sl CMObject} {\rm ob[0]} \\
 \hline  \hline
 $\cdots$ & {\tt CMObject} {\rm ob[n-1]} \\  $\cdots$ & {\sl CMObject} {\rm ob[n-1]} \\
 \cline{1-2}  \cline{1-2}
 \end{tabular} \\  \end{tabular} \\
   
   A mathematical programmer who wants to implement CMO on a server proceeds
 A mathematical programmer who wants to implement CMO on a server proceed  
 as follows.  as follows.
 \begin{enumerate}  \begin{enumerate}
 \item Look for the CMO list at the web cite \cite{openxm-web}.  \item Look for the CMO list at the web cite \cite{openxm-web}.
 If there is a CMO tht fits to her or his requirement, then use this CMO.  If there is a CMO that fits to her or his requirement, then use this CMO.
 \item If there is no suitable CMO, design a new CMO and register  \item If there is no suitable CMO, design a new CMO and register
 the new CMO to \cite{openxm-web} with a description and examples.  the new CMO to \cite{openxm-web} with a description and examples.
 \end{enumerate}  \end{enumerate}
   
   
   
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