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1.1       noro        1: % $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.9 2000/01/16 10:55:40 takayama Exp $
                      2:
                      3: \section{Data Format}
                      4:
                      5: OpenXM admits multiple mathematical encodings such as OpenMath, MP, CMO
                      6: (Common Mathematical Object format).
                      7: OpenXM itself does not exhibit a bias towards a particular encodings
                      8: as a main mathematical data carrier and an OpenXM compliant system do not need to
                      9: implement all possible data formats.
                     10: However  they should at least implement seven primitive
                     11: data types of the CMO, which are necessary to
                     12: carry several control informations such as a {\it mathcap}.
                     13: Mathcap is a list of supported CMO's, OpenXM stack machine codes,
                     14: and necessary extra informations.
                     15: If a program sends an OX messages unknown to its peer,
                     16: an unrecoverable error may occur.
                     17: By exchanging mathcaps, a program knows its peer's capability
                     18: and such an error can be avoided.
                     19: Mathcap is also defined as a CMO.
                     20: See \cite{noro-takayama} for the details.
                     21:
                     22: Encoding types of OX data are distinguished with tags
                     23: of OX messages.
                     24: For example,
                     25: an OX message with the tag
                     26: {\tt OX\_DATA} is followed by a CMO packet.
                     27: An OX message with the tag
                     28: {\tt OX\_DATA\_OPENMATH\_XML} is followed by
                     29: an OpenMath XML string.
                     30:
                     31: Let us explain the data format of CMO.
                     32: Any CMO packet consists of a header and a body.
                     33: The size of the header is 4 bytes that tags the data type of the body.
                     34: Data type tags are signed 32 bit integers which is called {\sl int32} in this
                     35: paper.
                     36: Following tags are registered in the OpenXM.
                     37: \begin{verbatim}
                     38: CMO_ERROR2, CMO_NULL, CMO_INT32, CMO_DATUM, CMO_STRING,
                     39: CMO_MATHCAP, CMO_LIST, CMO_MONOMIAL32, CMO_ZZ, CMO_QQ, CMO_ZERO,
                     40: CMO_DMS_GENERIC, CMO_DMS_OF_N_VARIABLES, CMO_RING_BY_NAME,
                     41: CMO_RECURSIVE_POLYNOMIAL, CMO_LIST_R, CMO_INT32COEFF,
                     42: CMO_DISTRIBUTED_POLYNOMIAL, CMO_POLYNOMIAL_IN_ONE_VARIABLE,
                     43: CMO_RATIONAL, CMO_64BIT_MACHINE_DOUBLE,
                     44: CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE, CMO_BIGFLOAT,
                     45: CMO_IEEE_DOUBLE_FLOAT, CMO_INDETERMINATE, CMO_TREE, CMO_LAMBDA
                     46: \end{verbatim}
                     47: The first seven primitive types should be implemented
                     48: on all OpenXM compliant systems.
                     49: The formats are as follows. \\
                     50: \begin{tabular}{|c|c|}
                     51: \hline
                     52: {\sl int32} {\tt CMO\_ERROR2} & {\sl CMObject} {\rm ob} \\
                     53: \hline
                     54: \end{tabular} \\
                     55: \begin{tabular}{|c|c|}
                     56: \hline
                     57: {\sl int32} {\tt CMO\_NULL}  \\
                     58: \hline
                     59: \end{tabular} \\
                     60: \begin{tabular}{|c|c|}
                     61: \hline
                     62: {\sl int32} {\tt CMO\_INT32}& {\sl int32} {\rm n}  \\
                     63: \hline
                     64: \end{tabular} \\
                     65: \begin{tabular}{|c|c|c|c|c|}
                     66: \hline
                     67: {\sl int32} {\tt CMO\_STRING}& {\sl int32} {\rm n} & {\sl byte} {\rm data[0]} $\cdots$ & {\sl byte} {\rm data[n-1]} \\  \hline
                     68: \end{tabular} \\
                     69: \begin{tabular}{|c|c|}
                     70: \hline
                     71: {\sl int32} {\tt CMO\_MATHCAP} & {\sl CMObject} {\rm ob} \\
                     72: \hline
                     73: \end{tabular} \\
                     74: \begin{tabular}{|c|c|c|c|c|}
                     75: \hline
                     76: {\sl int32} {\tt CMO\_LIST}& {\sl int32} {\rm n} & {\sl CMObject} {\rm ob[0]}
                     77: $\cdots$ & {\sl CMObject} {\rm ob[n-1]} \\  \hline
                     78: \end{tabular} \\
                     79:
                     80: As to the formats of other CMO's, see \cite{noro-takayama}.
                     81:
                     82: When one wants to implement CMO on a server, the person proceeds
                     83: as follows.
                     84: \begin{enumerate}
                     85: \item Look for the list of CMO's at the web cite \cite{openxm-web}.
                     86: If there is a CMO that fits to one's requirement, then use this CMO.
                     87: \item If there is no suitable CMO, design a new CMO and register
                     88: the new CMO to \cite{openxm-web} with a description and examples.
                     89: \end{enumerate}