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version 1.70, 1999/12/24 10:57:52 version 1.73, 1999/12/24 15:42:24
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 \documentclass{jarticle}  \documentclass{jarticle}
   
 %% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.69 1999/12/24 10:08:41 tam Exp $  %% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.72 1999/12/24 12:03:33 tam Exp $
   
 \usepackage{jssac}  \usepackage{jssac}
 \title{  \title{
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 \author{±ü ë ¡¡ ¹Ô ±û\affil{¿À¸ÍÂç³ØÂç³Ø±¡¼«Á³²Ê³Ø¸¦µæ²Ê}  \author{±ü ë ¡¡ ¹Ô ±û\affil{¿À¸ÍÂç³ØÂç³Ø±¡¼«Á³²Ê³Ø¸¦µæ²Ê}
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 \section{OpenXM ¥¹¥¿¥Ã¥¯¥Þ¥·¥ó}  \section{OpenXM ¥¹¥¿¥Ã¥¯¥Þ¥·¥ó}\label{sec:oxsm}
   
 OpenXM µ¬Ìó¤Ç¤Ï¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ç¤¢¤ë¤ÈÄêµÁ¤·¤Æ¤¤¤ë¡£°Ê²¼¡¢OpenXM  OpenXM µ¬Ìó¤Ç¤Ï¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ç¤¢¤ë¤ÈÄêµÁ¤·¤Æ¤¤¤ë¡£°Ê²¼¡¢OpenXM
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 \section{CMO ¤Î¥Ç¡¼¥¿¹½Â¤}  
   
   \section{CMO ¤Î¥Ç¡¼¥¿¹½Â¤}\label{sec:cmo}
   
 OpenXM µ¬Ìó¤Ç¤Ï¡¢¿ô³ØŪ¥ª¥Ö¥¸¥§¥¯¥È¤òɽ¸½¤¹¤ëÊýË¡¤È¤·¤Æ CMO ·Á¼°(Common  OpenXM µ¬Ìó¤Ç¤Ï¡¢¿ô³ØŪ¥ª¥Ö¥¸¥§¥¯¥È¤òɽ¸½¤¹¤ëÊýË¡¤È¤·¤Æ CMO ·Á¼°(Common
 Mathematical Object format)¤òÄêµÁ¤·¤Æ¤¤¤ë¡£¤³¤Î CMO ·Á¼°¤Ë¤·¤¿¤¬¤Ã¤¿¥Ç¡¼  Mathematical Object format)¤òÄêµÁ¤·¤Æ¤¤¤ë¡£¤³¤Î CMO ·Á¼°¤Ë¤·¤¿¤¬¤Ã¤¿¥Ç¡¼
 ¥¿¤Ï¡¢¼±Ê̻Ҥ¬ OX\_DATA ¤Ç¤¢¤ë¤è¤¦¤Ê¥á¥Ã¥»¡¼¥¸¤Î¥Ü¥Ç¥£¤Ë¤Ê¤ë¤³¤È¤òÁÛÄꤷ  ¥¿¤Ï¡¢¼±Ê̻Ҥ¬ OX\_DATA ¤Ç¤¢¤ë¤è¤¦¤Ê¥á¥Ã¥»¡¼¥¸¤Î¥Ü¥Ç¥£¤Ë¤Ê¤ë¤³¤È¤òÁÛÄꤷ
 ¤Æ¤¤¤ë¡£  ¤Æ¤¤¤ë¡£
   
 CMO ·Á¼°¤Ë¤ª¤±¤ë¥Ç¡¼¥¿¹½Â¤¤Ï¼¡¤Î¤è¤¦¤Ê¹½Â¤¤ò¤â¤Ä¡£  CMO ·Á¼°¤Ë¤ª¤±¤ë¥Ç¡¼¥¿¹½Â¤¤Ï¼¡¤Î¤è¤¦¤Ê¹½Â¤¤ò¤â¤Ä¡£
 \begin{verbatim}  
 ¥Ø¥Ã¥À     ¥Ü¥Ç¥£  
 \end{verbatim}  
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 \begin{verbatim}  \begin{tabular}{|c|c|} \hline
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 ÀâÌÀ¡£ÀâÌÀ¡£ÀâÌÀ¡£ÀâÌÀ¡£ÀâÌÀ¡£  \end{tabular}
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 OpenXM µ¬Ìó¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ëÍÍ¡¹¤Ê¥Ç¡¼¥¿¹½Â¤¤òÍý²ò¤¹¤ë½õ¤±¤Ë¤Ê¤ë¤È»×¤¨¤ë¤Î¤Ç¡¢  CMO ¤Ç¤Ï¡¢¥¿¥°¤Ë¤è¤Ã¤Æ¥Ü¥Ç¥£¤ÎÏÀÍýŪ¹½Â¤¤¬·èÄꤹ¤ë¡£¤¹¤Ê¤ï¤Á¡¢¥¿¥°¤Ï¤½¤ì
 ¤³¤³¤Ç¤Ï CMO ·Á¼°¤Î¿ÇÜĹÀ°¿ô¤Î¥Ç¡¼¥¿¹½Â¤¤Ë¤Ä¤¤¤Æ¤Î¤ßÀâÌÀ¤¹¤ë¡£  ¤¾¤ì¤Î¥Ç¡¼¥¿¹½Â¤¤È1ÂÐ1¤ËÂбþ¤¹¤ë¼±Ê̻ҤǤ¢¤ë¡£¤½¤ì¤¾¤ì¤ÎÏÀÍýŪ¹½Â¤¤Ï
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 CMO ·Á¼°¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë¥Ç¡¼¥¿¤Ï¿ÇÜĹÀ°¿ô°Ê³°¤Ë¤â  
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 ¤è¤¯»È¤ï¤ì¤ë¤È»×¤ï¤ì¤ë CMO ·Á¼°¤Î¥¿¥°¤ò¤¢¤²¤Æ¤ª¤¯¡£  
 \begin{verbatim}  \begin{verbatim}
 #define CMO_INT32    2 /* (CMO ·Á¼°¤Î)32 ¥Ó¥Ã¥ÈÀ°¿ô */  #define CMO_ERROR2 0x7f000002
 #define CMO_STRING   4 /* ʸ»úÎó                    */  #define CMO_NULL   1
 #define CMO_MATHCAP  5 /* mathcap(¸å½Ò)             */  #define CMO_INT32  2
 #define CMO_LIST    17 /* ¥ê¥¹¥È¹½Â¤                */  #define CMO_DATUM  3
 #define CMO_ZZ      20 /* ¿ÇÜĹÀ°¿ô                */  #define CMO_STRING 4
   #define CMO_MATHCAP 5
   
   #define CMO_START_SIGNATURE    0x7fabcd03
   #define     CMO_ARRAY  16
   #define     CMO_LIST 17
   #define     CMO_ATOM 18
   #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}  \end{verbatim}
 ¥¿¥°°Ê¹ß¤Ï¥Ç¡¼¥¿ËÜÂΤǤ¢¤ê¡¢¥Ç¡¼¥¿ËÜÂΤι½Â¤¤Ï¥Ç¡¼¥¿¤Î¼ïÎà¤Ë¤è¤Ã¤Æ°Û¤Ê¤ë¡£  
 À°¿ôÃÍ $123456789$ ¤òɽ¤¹ CMO\_INT32 ¤Ï  
 \begin{tabular}{|c|c|} \hline  
 CMO\_INT32 & $123456789$        \\ \hline  
 \end{tabular}  
 ¤ÈÄêµÁ¤µ¤ì¤Æ¤¤¤ë¤¬¡¢¤³¤ì¤ò°Ê¸å (CMO\_INT32, 123456789) ¤È¤·¤Æɽ¤¹¡£  
   
   ¤³¤ÎÃæ¤Ç CMO\_INT32, ... ¤Ç¼±Ê̤µ¤ì¤ë¥ª¥Ö¥¸¥§¥¯¥È¤ÏºÇ¤â´ðËÜŪ¤Ê¥ª¥Ö¥¸¥§
   ¥¯¥È¤Ç¤¢¤Ã¤Æ¡¢¤¹¤Ù¤Æ¤Î OpenXM Âбþ¥·¥¹¥Æ¥à¤Ë¼ÂÁõ¤µ¤ì¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤¡£
   
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 OpenXM µ¬Ìó¤Ç¤Ï¥Ð¥¤¥È¥¹¥È¥ê¡¼¥à¤Ç 32 bit ¤ÎÀ°¿ô 20 ¤ò  ¤³¤ÎÏÀʸ¤Ç¤Ï¡¢Âçʸ»ú¤Ç CMO\_INT32 ¤È½ñ¤¤¤¿¾ì¹ç¤Ë¤Ï¡¢¾åµ­¤ÇÄêµÁ¤·¤¿¼±ÊÌ»Ò
 {\tt 00 00 00 14} ¤Èɽ¤¹ÊýË¡¤È {\tt 14 00 00 00} ¤Èɽ¤¹ÊýË¡¤¬¤¢¤ë¡£  ¤òɽ¤ï¤¹¡£¤Þ¤¿ CMO\_INT32 ¤Ç¼±Ê̤µ¤ì¤ë¥ª¥Ö¥¸¥§¥¯¥È¤Î¥¯¥é¥¹(¤¢¤ë¤¤¤Ï¥Ç¡¼
 ¤³¤Îɽ¸½ÊýË¡¤Î°ã¤¤¤Ï¥¯¥é¥¤¥¢¥ó¥È¤È¥µ¡¼¥Ð¤ÎºÇ½é¤ÎÀܳ»þ¤Ë  ¥¿¹½Â¤)¤ò cmo\_int32 ¤È¾®Ê¸»ú¤Çɽ¤ï¤¹¤³¤È¤Ë¤¹¤ë¡£
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 ¤Þ¤¿¡¢Éé¤Î¿ô¤òɽ¸½¤¹¤ëɬÍפ¬¤¢¤ë¤È¤­¤Ë¤Ï¡¢  
 2 ¤ÎÊä¿ôɽ¸½¤ò»È¤¦¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£  
   
 CMO ·Á¼°¤Î¿ÇÜĹÀ°¿ô¤Ï¡¢ Gnu MP¥é¥¤¥Ö¥é¥êÅù¤ò»²¹Í¤Ë¤·¤Æ¤ª¤ê¡¢  ¤µ¤Æ cmo ¤òɽ¸½¤¹¤ë¤¿¤á¤Î°ì¤Ä¤Îµ­Ë¡¤òƳÆþ¤¹¤ë¡£¤³¤Îµ­Ë¡¤Ï CMO expression
 Éä¹æÉÕ¤­ÀäÂÐÃÍɽ¸½¤òÍѤ¤¤Æ¤¤¤ë¡£  ¤È¸Æ¤Ð¤ì¤Æ¤¤¤ë¡£¤½¤ÎÀµ³Î¤Ê·Á¼°ÅªÄêµÁ¤Ï \cite{OpenXM-1999} ¤ò»²¾È¤¹¤ë¤³¤È¡£
 ¥¿¥°°Ê¹ß¤Î·Á¼°¤Ï¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¡£  
   
 \begin{tabular}{|c|c|c|c|c|} \hline  ¤Þ¤º CMO expssion ¤Ï Lisp É÷ɽ¸½¤Î°ì¼ï¤Ç¡¢ cmo ¤ò³ç¸Ì¤Ç°Ï¤ó¤À¥ê¥¹¥È¤È¤·
 $f$ & $b_0$ & $b_1$ & $\cdots$ & $b_{n-1}$ \\ \hline  ¤Æɽ¸½¤¹¤ë¡£¤½¤ì¤¾¤ì¤ÎÍ×ÁǤϥ«¥ó¥Þ¤Ç¶èÀڤ롣
 \end{tabular}  Î㤨¤Ð¡¢
   \begin{quote}
   (17, {\sl int32}, (CMO\_NULL), (2, {\sl int32} $n$))
   \end{quote}
   ¤Ï CMO expression ¤Ç¤¢¤ë¡£¤³¤³¤Ç¡¢¾®Ê¸»ú¤Î¼ÐÂΤÇɽ¤µ¤ì¤¿``{\sl int32}''
   ¤Ï 4¥Ð¥¤¥È¤ÎǤ°Õ¤Î¥Ç¡¼¥¿¤òɽ¤¹µ­¹æ¤Ç¤¢¤ê¡¢``{\sl int32} $n$'' ¤ÏƱ¤¸¤¯ 4
   ¥Ð¥¤¥È¤Î¥Ç¡¼¥¿¤Ç¤¢¤ë¤¬°Ê²¼¤ÎÀâÌÀ¤Ç $n$ ¤Èɽ¤¹¤³¤È¤ò¼¨¤¹¡£¤Þ¤¿¿ô»ú 17, 2
   ¤Ê¤É¤Ï 4¥Ð¥¤¥È¤Î¥Ç¡¼¥¿¤ÇÀ°¿ôÃͤȤ·¤Æ¤ß¤¿¤È¤­¤ÎÃͤò°ÕÌ£¤¹¤ë¡£CMO\_NULL ¤Ï
   ¼±ÊÌ»Ò(¤¹¤Ê¤ï¤Á¿ô»ú 1 ¤ÈÅù²Á)¤Ç¤¢¤ë¡£¤³¤Îµ­Ë¡¤«¤é¾åµ­¤Î¥Ç¡¼¥¿¤Ï 20 ¥Ð¥¤
   ¥È¤ÎÂ礭¤µ¤Î¥Ç¡¼¥¿¤Ç¤¢¤ë¤³¤È¤¬Ê¬¤«¤ë¡£
   
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 $f$ ¤ÏÉä¹æÉÕ¤­ 32 ¥Ó¥Ã¥ÈÀ°¿ô¤ò¡¢  \begin{quote}
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