version 1.1, 1999/12/23 10:25:08 |
version 1.4, 2000/01/11 05:35:48 |
|
|
% $OpenXM$ |
% $OpenXM: OpenXM/doc/issac2000/data-format.tex,v 1.3 2000/01/03 04:27:52 takayama Exp $ |
|
|
|
\section{Data Format} (Ohara) |
|
|
|
OpenXM admits multiple math encodings such as OpenMath, MP, CMO |
|
(Common Mathematical Object format). |
|
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 |
|
implement all possible data formats. |
|
A server or a client does not necessarily implement full specifications |
|
of OpenXM. |
|
However, if a program sends an OX data or an OX command unknown to its peer, |
|
an unrecoverable error may occur. |
|
To avoid such a case OpenXM provides a scheme not |
|
to send an OX message unknown to peers. |
|
It is realized by exchanging a list of |
|
supported CMO's, OpenXM stackmachine codes, and necessary extra informations. |
|
The list is called {\it mathcap}. |
|
Mathcap is also defined as a CMO and its elements are 32bit integers |
|
or strings. |
|
|
|
Math encoding types of OX data are distinguished with tags |
|
of OX messages. |
|
For example, |
|
an OX message with the tag |
|
OX\_DATA is followed by a CMO packet. |
|
An OX message with the tag |
|
OX\_DATA\_OPENMATH\_XML is followed by |
|
an OpenMath XML string and its length. |
|
|
|
All OpenXM compliant systems should implement 7 primitive data types |
|
of the CMO. |
|
These are used not only to express mathematical objects, but also |
|
indispensable to carry control informations such as mathcap. |
|
CMO is an original methematical data encoding system of the OpenXM project. |
|
Let us explain the data format of CMO. |
|
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. |
|
Data type tags are signed 32 bit integers which is called {\sl int32} in this |
|
paper. |
|
Following tags are registered in the OpenXM for now. |
|
\begin{verbatim} |
|
#define CMO_ERROR2 0x7f000002 |
|
#define CMO_NULL 1 |
|
#define CMO_INT32 2 |
|
#define CMO_DATUM 3 |
|
#define CMO_STRING 4 |
|
#define CMO_MATHCAP 5 |
|
#define CMO_LIST 17 |
|
|
|
#define CMO_MONOMIAL32 19 |
|
#define CMO_ZZ 20 |
|
#define CMO_QQ 21 |
|
#define CMO_ZERO 22 |
|
#define CMO_DMS_GENERIC 24 |
|
#define CMO_DMS_OF_N_VARIABLES 25 |
|
#define CMO_RING_BY_NAME 26 |
|
#define CMO_RECURSIVE_POLYNOMIAL 27 |
|
#define CMO_LIST_R 28 |
|
#define CMO_INT32COEFF 30 |
|
#define CMO_DISTRIBUTED_POLYNOMIAL 31 |
|
#define CMO_POLYNOMIAL_IN_ONE_VARIABLE 33 |
|
#define CMO_RATIONAL 34 |
|
#define CMO_64BIT_MACHINE_DOUBLE 40 |
|
#define CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE 41 |
|
#define CMO_128BIT_MACHINE_DOUBLE 42 |
|
#define CMO_ARRAY_OF_128BIT_MACHINE_DOUBLE 43 |
|
#define CMO_BIGFLOAT 50 |
|
#define CMO_IEEE_DOUBLE_FLOAT 51 |
|
#define CMO_INDETERMINATE 60 |
|
#define CMO_TREE 61 |
|
#define CMO_LAMBDA 62 |
|
\end{verbatim} |
|
The first seven types should be implemented on all OpenXM compliant systems. |
|
The format of the first seven CMO's are as follows. \\ |
|
\begin{tabular}{|c|c|} |
|
\hline |
|
{\tt int32 CMO\_ERROR2} & {\sl CMObject} {\rm ob} \\ |
|
\hline |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|} |
|
\hline |
|
{\tt int32 CMO\_NULL} \\ |
|
\hline |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|} |
|
\hline |
|
{\tt int32 CMO\_INT32}& {\tt int32} {\rm n} \\ |
|
\hline |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|c|} |
|
\hline |
|
{\tt int32 CMO\_DATUM}& {\tt int32} {\rm n} & {\tt byte} {\rm data[0]} \\ |
|
\hline |
|
$\cdots$ & {\tt byte} {\rm data[n-1]} \\ |
|
\cline{1-2} |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|c|} |
|
\hline |
|
{\tt int32 CMO\_STRING}& {\tt int32} {\rm n} & {\tt byte} {\rm data[0]} \\ |
|
\hline |
|
$\cdots$ & {\tt byte} {\rm data[n-1]} \\ |
|
\cline{1-2} |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|} |
|
\hline |
|
{\tt int32 CMO\_MATHCAP} & {\it CMObject} {\rm ob} \\ |
|
\hline |
|
\end{tabular} \\ |
|
\begin{tabular}{|c|c|c|} |
|
\hline |
|
{\tt int32 CMO\_LIST}& {\tt int32} {\rm n} & {\tt CMObject} {\rm ob[0]} \\ |
|
\hline |
|
$\cdots$ & {\tt CMObject} {\rm ob[n-1]} \\ |
|
\cline{1-2} |
|
\end{tabular} \\ |
|
|
|
|
|
A mathematical programmer who wants to implement CMO on a server proceeds |
|
as follows. |
|
\begin{enumerate} |
|
\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. |
|
\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. |
|
\end{enumerate} |
|
|
|
|
|
|