version 1.2, 2000/01/02 07:32:11 |
version 1.9, 2000/01/16 10:55:40 |
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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 1.8 2000/01/16 06:02:41 takayama Exp $ |
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\section{Data Format} (Ohara) |
\section{Data Format} |
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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 |
However they should at least implement seven primitive |
of OpenXM. |
data types of the CMO, which are necessary to |
However, if a program sends an OX data or an OX command unknown to its peer, |
carry several control informations such as a {\it mathcap}. |
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Mathcap is a list of supported CMO's, OpenXM stack machine codes, |
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and necessary extra informations. |
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If a program sends an OX messages unknown to its peer, |
an unrecoverable error may occur. |
an unrecoverable error may occur. |
To avoid such a case OpenXM provides a scheme not |
By exchanging mathcaps, a program knows its peer's capability |
to send an OX message unknown to peers. |
and such an error can be avoided. |
It is realized by exchanging the list of |
Mathcap is also defined as a CMO. |
supported CMO's, OpenXM stack machine codes, and necessary extra informations. |
See \cite{noro-takayama} for the details. |
The list is called mathcap. |
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Mathcap is also defined as a CMO and the elements are 32bit integers |
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or strings. |
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Math encoding types of OX data are distinguished with tags |
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. |
{\tt 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 |
{\tt OX\_DATA\_OPENMATH\_XML} is followed by |
OpenMath XML string and its length. |
an OpenMath XML string. |
All OpenXM compliant systems should implement 7 primitive data types |
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of CMO. |
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These are used not only to express mathematical objects, but also |
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indespensable to carry control informations such as mathcap. |
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CMO is an original methematical data encoding system of the OpenXM project. |
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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. |
Data type tags are signed 32 bit integers which is called {\sl int32} in this |
Data type tags are signed 32 bit integers which is called {\sl int32} in this |
paper. |
paper. |
Following tags are registered in the OpenXM for now. |
Following tags are registered in the OpenXM. |
\begin{verbatim} |
\begin{verbatim} |
#define CMO_ERROR2 0x7f000002 |
#define CMO_ERROR2 0x7f000002 |
#define CMO_NULL 1 |
#define CMO_NULL 1 |
Line 46 Following tags are registered in the OpenXM for now. |
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Line 42 Following tags are registered in the OpenXM for now. |
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#define CMO_STRING 4 |
#define CMO_STRING 4 |
#define CMO_MATHCAP 5 |
#define CMO_MATHCAP 5 |
#define CMO_LIST 17 |
#define CMO_LIST 17 |
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#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 61 Following tags are registered in the OpenXM for now. |
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Line 58 Following tags are registered in the OpenXM for now. |
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#define CMO_RATIONAL 34 |
#define CMO_RATIONAL 34 |
#define CMO_64BIT_MACHINE_DOUBLE 40 |
#define CMO_64BIT_MACHINE_DOUBLE 40 |
#define CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE 41 |
#define CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE 41 |
#define CMO_128BIT_MACHINE_DOUBLE 42 |
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#define CMO_ARRAY_OF_128BIT_MACHINE_DOUBLE 43 |
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#define CMO_BIGFLOAT 50 |
#define CMO_BIGFLOAT 50 |
#define CMO_IEEE_DOUBLE_FLOAT 51 |
#define CMO_IEEE_DOUBLE_FLOAT 51 |
#define CMO_INDETERMINATE 60 |
#define CMO_INDETERMINATE 60 |
#define CMO_TREE 61 |
#define CMO_TREE 61 |
#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 primitive types should be implemented |
The format of the first severn CMO's are as follows. \\ |
on all OpenXM compliant systems. |
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The formats 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} \\ |
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As to the formats of other CMO's, see \cite{noro-takayama}. |
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A mathematical programmer who wants to implement CMO on a server proceed |
When one wants to implement CMO on a server, the person proceeds |
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 list of CMO's 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 one's 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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