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version 1.44, 1999/12/22 15:04:49 version 1.80, 1999/12/25 04:08:50
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 \documentclass{jarticle}  \documentclass{jarticle}
   
 \title{¥¿¥¤¥È¥ë̤Äê}  %% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.79 1999/12/24 21:56:37 tam Exp $
 \author{  
 Á°Àî ¾­½¨\thanks{¿À¸ÍÂç³ØÍý³ØÉô¿ô³Ø²Ê},  \usepackage{jssac}
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 }  }
 \date{1999ǯ11·î25Æü}  
 %\pagestyle{empty}  
   
   \author{±ü ë ¡¡ ¹Ô ±û\affil{¿À¸ÍÂç³ØÂç³Ø±¡¼«Á³²Ê³Ø¸¦µæ²Ê}
                   \mail{okutani@math.sci.kobe-u.ac.jp}
     \and  ¾® ¸¶ ¡¡ ¸ù Ǥ\affil{¶âÂôÂç³ØÍý³ØÉô}
                   \mail{ohara@kappa.s.kanazawa-u.ac.jp}
     \and  ¹â »³ ¡¡ ¿® µ£\affil{¿À¸ÍÂç³ØÍý³ØÉô}
                   \mail{takayama@math.sci.kobe-u.ac.jp}
     \and  ÅÄ Â¼ ¡¡ ¶³ »Î\affil{¿À¸ÍÂç³ØÂç³Ø±¡¼«Á³²Ê³Ø¸¦µæ²Ê}
                   \mail{tamura@math.sci.kobe-u.ac.jp}
     \and  Ìî Ϥ ¡¡ Àµ ¹Ô\affil{ÉÙ»ÎÄ̸¦µæ½ê}
                   \mail{noro@para.flab.fujitsu.co.jp}
     \and  Á° Àî ¡¡ ¾­ ½¨\affil{¿À¸ÍÂç³ØÍý³ØÉô}
                   \mail{maekawa@math.sci.kobe-u.ac.jp}
   }
   \art{}
   
 \begin{document}  \begin{document}
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   \item
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 \section{OpenXM ¤Î·×»»¤Î¿Ê¹ÔÊýË¡}  
   
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 {\Huge °Ê²¼¡¢½ñ¤­Ä¾¤·}  \begin{verbatim}
   #define SM_popSerializedLocalObject               258
   #define SM_popCMO                                 262
   #define SM_popString                              263
   
 ¥¯¥é¥¤¥¢¥ó¥È¤¬¥µ¡¼¥Ð¤Ø·×»»¤ò¹Ô¤Ê¤ï¤»¡¢·ë²Ì¤òÆÀ¤ë¤È¤¤¤¦¼ê½ç¤òÄɤäƤ¤¤¯¤È¡¢  #define SM_mathcap                                264
 ¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¡£  #define SM_pops                                   265
   #define SM_setName                                266
   #define SM_evalName                               267
   #define SM_executeStringByLocalParser             268
   #define SM_executeFunction                        269
   #define SM_beginBlock                             270
   #define SM_endBlock                               271
   #define SM_shutdown                               272
   #define SM_setMathCap                             273
   #define SM_executeStringByLocalParserInBatchMode  274
   #define SM_getsp                                  275
   #define SM_dupErrors                              276
   
 \begin{enumerate}  #define SM_DUMMY_sendcmo                          280
 \item   ¤Þ¤º¡¢¥¯¥é¥¤¥¢¥ó¥È¤¬¥µ¡¼¥Ð¤Ø·×»»¤µ¤»¤¿¤¤¥Ç¡¼¥¿¤òÁ÷¤ë¡£  #define SM_sync_ball                              281
         ¥µ¡¼¥Ð¤ÏÁ÷¤é¤ì¤Æ¤­¤¿¥Ç¡¼¥¿¤ò¥¹¥¿¥Ã¥¯¤ËÀѤࡣ  
 \item   ¥¯¥é¥¤¥¢¥ó¥È¤¬¥µ¡¼¥Ð¤Ë¡Ö·×»»¤ò¹Ô¤Ê¤¦Æ°ºî¤ËÂбþ¤·¤¿¥Ç¡¼¥¿¡×¤ò  
         Á÷¤ë¤È¡¢¥µ¡¼¥Ð¤ÏɬÍפʤÀ¤±¥¹¥¿¥Ã¥¯¤«¤é¥Ç¡¼¥¿¤ò¼è¤ê½Ð¤·¡¢  
         ¼Â¹Ô¤·¤¿·×»»¤Î·ë²Ì¤ò¥¹¥¿¥Ã¥¯¤ËÀѤࡣ  
 \item   ºÇ¸å¤Ë¡Ö¥Ç¡¼¥¿¤ò¼è¤ê½Ð¤·Á÷¿®¤ò¹Ô¤Ê¤¦Ì¿Îá¤ËÂбþ¤·¤¿¥Ç¡¼¥¿¡×¤ò  
         ¥µ¡¼¥Ð¤ØÁ÷¤ë¤È¡¢¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¤«¤é·×»»·ë²Ì¤ÎÆþ¤Ã¤Æ¤¤¤ë  
         ¥Ç¡¼¥¿¤ò¼è¤ê½Ð¤·¡¢¥¯¥é¥¤¥¢¥ó¥È¤ØÁ÷½Ð¤¹¤ë¡£  
 \end{enumerate}  
   
   #define SM_control_kill                          1024
   #define SM_control_to_debug_mode                 1025
   #define SM_control_exit_debug_mode               1026
   #define SM_control_ping                          1027
   #define SM_control_start_watch_thread            1028
   #define SM_control_stop_watch_thread             1029
   #define SM_control_reset_connection              1030
   \end{verbatim}
   
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 CMO ·Á¼°¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë MathCap ¥Ç¡¼¥¿¤Ï  \begin{verbatim}
 %Íý²ò²Äǽ¤Ê¥á¥Ã¥»¡¼¥¸¤Î  #define CMO_ERROR2  0x7f000002
 ¼õ¤±¼è¤ë¤³¤È¤¬¤Ç¤­¤ë¥Ç¡¼¥¿·Á¼°¤òɽ¤¹¥Ç¡¼¥¿¤Ç¤¢¤ê¡¢  #define CMO_NULL    1
 Í׵ᤵ¤ì¤ì¤Ð¥µ¡¼¥Ð¤Ï¥µ¡¼¥Ð¼«¿È¤Î MathCap ¥Ç¡¼¥¿¤ò¥¹¥¿¥Ã¥¯¤ËÀѤࡣ  #define CMO_INT32   2
 ¤Þ¤¿¡¢¥¯¥é¥¤¥¢¥ó¥È¤«¤é MathCap ¥Ç¡¼¥¿¤ò¥µ¡¼¥Ð¤ØÁ÷¤ë¤³¤È¤â¤Ç¤­¡¢  #define CMO_DATUM   3
 MathCap ¥Ç¡¼¥¿¤ò¥µ¡¼¥Ð¤È¥¯¥é¥¤¥¢¥ó¥È¤Î´Ö¤Ç¸ò´¹¤¹¤ë¤³¤È¤Ë¤è¤Ã¤Æ¡¢  #define CMO_STRING  4
 ¤ª¸ß¤¤¤ËÁê¼ê¦¤¬¼õ¤±¼è¤ë¤³¤È¤¬¤Ç¤­¤Ê¤¤¥Ç¡¼¥¿·Á¼°¤Ç  #define CMO_MATHCAP 5
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 32 bit À°¿ô¡¢Ê¸»úÎ󡢥ꥹ¥È¹½Â¤¤¬»È¤ï¤ì¤Æ¤ª¤ê¡¢  
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 OpenXM ÂбþÈǤΠasir ¥µ¡¼¥Ð¤Ç¤¢¤ë ox\_asir ¤¬ÊÖ¤¹ MathCap ¤ò°Ê²¼¤Ë¼¨¤¹¡£  #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
   
 %¤Ê¤ª¡¢ $a_1$, $a_2$, $\cdots$, $a_n$ ¤òÍ×ÁÇ¤Ë  #define CMO_INT32COEFF                 30
 %»ý¤Ä¥ê¥¹¥È¹½Â¤¤ò {\tt [$a_1$, $a_2$, $\cdots$, $a_n$]} ¡¢  #define CMO_DISTRIBUTED_POLYNOMIAL     31
 %ʸ»úÎó ``string'' ¤ò {\tt "string"} ¡¢ 32 bit À°¿ô¤ò  #define CMO_POLYNOMIAL_IN_ONE_VARIABLE 33
 %¤½¤ì¤ËÂбþ¤¹¤ë 10 ¿Ê¿ô¤ÎÀ°¿ô¤Ç¼¨¤¹¡£  #define CMO_RATIONAL                   34
   
 %¢­¼ê¤Çºî¤Ã¤¿¤Î¤Ç´Ö°ã¤¨¤Æ¤¤¤ë²ÄǽÀ­¤¢¤ê¡£  #define CMO_64BIT_MACHINE_DOUBLE           40
 %%¸Å¤¤¥Ð¡¼¥¸¥ç¥ó¡£º¹¤·Âؤ¨¤ÎɬÍפ¢¤ê¡£  #define CMO_ARRAY_OF_64BIT_MACHINE_DOUBLE  41
 \begin{verbatim}  #define CMO_128BIT_MACHINE_DOUBLE          42
 [ [199901160,"ox_asir"],  #define CMO_ARRAY_OF_128BIT_MACHINE_DOUBLE 43
   [276,275,258,262,263,266,267,268,274  
     ,269,272,265,264,273,300,270,271],  #define CMO_BIGFLOAT          50
   [ [514,[1,2,3,4,5,2130706433,2130706434  #define CMO_IEEE_DOUBLE_FLOAT 51
           ,17,19,20,21,22,24,25,26,31,27,33,60]],  
     [2144202544,[0,1]]  #define CMO_INDETERMINATE 60
   ]  #define CMO_TREE          61
 ]  #define CMO_LAMBDA        62
 \end{verbatim}  \end{verbatim}
   
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 ¼¡¤Î {\tt [276,275,$\cdots$,271]} ¤ÎÉôʬ¤Ï  ¤³¤ì¤é¤Ë¤Ä¤¤¤Æ¤Î²òÀâ¤ò¹Ô¤¦Á°¤Ëµ­Ë¡¤Ë¤Ä¤¤¤Æ¡¢¾¯¤·ÀâÌÀ¤·¤Æ¤ª¤¯¡£
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 ¤³¤Î¥ê¥¹¥È¤Ë 20 ¤¬´Þ¤Þ¤ì¤Æ¤¤¤ë¤Î¤Ç¡¢  
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 %%¤³¤Î¥ê¥¹¥È¤ÎÍ×ÁǤϤޤ¿¥ê¥¹¥È¤È¤Ê¤Ã¤Æ¤ª¤ê¡¢  ¤Þ¤º CMO expssion ¤Ï Lisp É÷ɽ¸½¤Î°ì¼ï¤Ç¡¢ cmo ¤ò³ç¸Ì¤Ç°Ï¤ó¤À¥ê¥¹¥È¤È¤·
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 %{\tt [514,[1, 2, $\cdots$]]} ¤ÎºÇ½é¤Î 514 ¤Ï¤³¤Î¥ê¥¹¥È¤¬ CMO ·Á¼°  \begin{quote}
 %¤Ç¤ÎÍý²ò²Äǽ¤Ê¥Ç¡¼¥¿¤òɽ¤·¤Æ¤¤¤ë¤³¤È¤ò¼¨¤·¤Æ¤ª¤ê¡¢  (17, {\sl int32}, (CMO\_NULL), (2, {\sl int32} $n$))
 %¤½¤Î¸å¤Î¥ê¥¹¥È¤Ç¤Ï CMO ÁؤÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë¥Ç¡¼¥¿¤Î¤¦¤Á¡¢  \end{quote}
 %Íý²ò²Äǽ¤Ê¥Ç¡¼¥¿¤Î¥¿¥°¤¬Ê¤ó¤Ç¤¤¤ë¡£  ¤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
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 Ãí°Õ¤¹¤ëɬÍפ¬¤¢¤ë¡£  cmo\_int32 := (CMO\_INT32,  {\sl int32} $a$)
   \end{quote}
   
   %{\Huge ƱÍÍ¤Ë cmo\_string, cmo\_list ¤Ê¤É¤òÄêµÁ}
   
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   ¤³¤ì¤òÍѤ¤¤Æ¡¢ cmo\_string, cmo\_list ¤òÄêµÁ¤¹¤ë¡£
   
   \begin{quote}
   cmo\_string := (CMO\_STRING, {\sl int32} $len$, {\sl string} $str$) \\
   cmo\_list := (CMO\_LIST, {\sl int32} $n$, {\sl cmo} $ob_1$,
                   {\sl cmo} $ob_2$, $\cdots$,{\sl cmo} $ob_n$)
   \end{quote}
   
   ¤³¤ì¤Ï¤½¤ì¤¾¤ìŤµ $len$ ¤Îʸ»úÎó $str$ ¤È¡¢
   $ob_1$, $ob_2$, $\cdots$, $ob_n$ ¤«¤é¤Ê¤ëŤµ $n$ ¤Î¥ê¥¹¥È¤òɽ¤¹¡£
   
   
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   % Àè¤Û¤É¤Î¡¢ (CMO\_INT32, 123456789) ¤ò¥Í¥Ã¥È¥ï¡¼¥¯¥Ð¥¤¥È¥ª¡¼¥À¡¼¤Ç
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   %       {\tt 00 00 00 04 00 00 00 06 4f 70 65 6e 58 4d}
   % \end{center}
   % ¤È¤Ê¤ë¡£
   
   % CMO ·Á¼°¤Î¿ÇÜĹÀ°¿ô¤Ï¡¢ Gnu MP¥é¥¤¥Ö¥é¥êÅù¤ò»²¹Í¤Ë¤·¤Æ¤ª¤ê¡¢
   % Éä¹æÉÕ¤­ÀäÂÐÃÍɽ¸½¤òÍѤ¤¤Æ¤¤¤ë¡£
   % ¥¿¥°°Ê¹ß¤Î·Á¼°¤Ï¼¡¤Î¤è¤¦¤Ë¤Ê¤ë¡£
   
   % \begin{tabular}{|c|c|c|c|c|} \hline
   % $f$ & $b_0$ & $b_1$ & $\cdots$ & $b_{n-1}$ \\ \hline
   % \end{tabular}
   
   % ¤³¤³¤Ç¡¢ 1 ¤Ä¤ÎÏÈ¤Ï 4 ¥Ð¥¤¥È¤òɽ¤·¡¢
   % $f$ ¤ÏÉä¹æÉÕ¤­ 32 ¥Ó¥Ã¥ÈÀ°¿ô¤ò¡¢
   % $b_0$, $b_1$, $\cdots$, $b_{n-1}$ ¤ÏÉä¹æ¤Ê¤· 32 ¥Ó¥Ã¥ÈÀ°¿ô¤òɽ¤·¤Æ¤¤¤ë¡£
   % ¤µ¤é¤Ë¡¢ $|f| = n$ ¤¬À®¤êΩ¤¿¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤¡£
   % ¤³¤Î¥ª¥Ö¥¸¥§¥¯¥È¤Ï
   % \[ \mbox{sgn}(f) \times \{ b_0 (2^{32})^0 + b_1 (2^{32})^1 + \cdots
   %       + b_{n-1} (2^{32})^{n-1} \}     \]
   % ¤È¤¤¤¦À°¿ô¤Ç¤¢¤ë¤ÈÄêµÁ¤µ¤ì¤Æ¤¤¤ë¡£
   % ¤¿¤À¤·¡¢
   % \[ \mbox{sgn}(f) = \left\{ \begin{array}{ll}
   %         1       & f>0 \\
   %         0       & f=0 \\
   %         -1      & f<0 \\ \end{array} \right.  \]
   % ¤Ç¤¢¤ë¡£
   
   % ¤³¤³¤Ç¶ñÂÎÎã¤ò¤À¤½¤¦¡£
   % $4294967298 = 1 \times 2^{32} + 2$ ¤ò CMO ·Á¼°¤Î
   % ¥Í¥Ã¥È¥ï¡¼¥¯¥Ð¥¤¥È¥ª¡¼¥À¡¼¡¢Â¿ÇÜĹÀ°¿ô¤Çɽ¸½¤¹¤ë¤È¡¢
   % \begin{center}
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   % \end{center}
   % ¤È¤Ê¤ë¡£¤Þ¤¿¡¢Æ±¤¸É½¸½ÊýË¡¤Ç $-1$ ¤òɽ¸½¤¹¤ë¤È¡¢
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   % \end{center}
   % ¤È¤Ê¤ë¡£
   
   
   \section{mathcap ¤Ë¤Ä¤¤¤Æ}
   
   OpenXM µ¬Ìó¤Ç¤Ï¡¢ÄÌ¿®»þ¤ËÍѤ¤¤é¤ì¤ë¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤ò³Æ¥½¥Õ¥È¥¦¥§¥¢¤¬À©
   ¸Â¤¹¤ëÊýË¡¤òÍÑ°Õ¤·¤Æ¤¤¤ë¡£¤³¤ì¤Ï³Æ¥½¥Õ¥È¥¦¥§¥¢¤Î¼ÂÁõ¤Ë¤è¤Ã¤Æ¤Ï¤¹¤Ù¤Æ¤Î¥á¥Ã
   ¥»¡¼¥¸¤ò¥µ¥Ý¡¼¥È¤¹¤ë¤Î¤¬º¤Æñ¤Ê¾ì¹ç¤¬¤¢¤ë¤«¤é¤Ç¤¢¤ë¡£¤Þ¤¿¡¢³Æ¥½¥Õ¥È¥¦¥§¥¢
   ¤Ç¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤ò³ÈÄ¥¤·¤¿¤¤¾ì¹ç¤Ë¤âÍ­¸ú¤Ç¤¢¤ë¡£¤³¤ÎÀ©¸Â(¤¢¤ë¤¤¤Ï³ÈÄ¥)
   ¤Ï mathcap ¤È¸Æ¤Ð¤ì¤ë¥Ç¡¼¥¿¹½Â¤¤Ë¤è¤Ã¤Æ¹Ô¤ï¤ì¤ë¡£¤³¤ÎÀá¤Ç¤Ï mathcap ¤Î¥Ç¡¼
   ¥¿¹½Â¤¤È¡¢¶ñÂÎŪ¤Ê¥á¥Ã¥»¡¼¥¸¤ÎÀ©¸Â¤Î¼ê³¤­¤Ë¤Ä¤¤¤ÆÀâÌÀ¤¹¤ë¡£
   
   ¤Ç¤Ï¡¢¼ê³¤­¤Ë¤Ä¤¤¤ÆÀâÌÀ¤·¤è¤¦¡£
   
   Âè°ì¤Ë¥µ¡¼¥Ð¤Îµ¡Ç½¤òÀ©¸Â¤¹¤ë¤Ë¤Ï¼¡¤Î¤è¤¦¤Ë¤¹¤ë¡£¥¯¥é¥¤¥¢¥ó¥È¤¬ mathcap
   ¥ª¥Ö¥¸¥§¥¯¥È¤ò¥µ¡¼¥Ð¤ØÁ÷¤ë¤È¡¢¥µ¡¼¥Ð¤Ï¼õ¤±¼è¤Ã¤¿mathcap ¤ò¥¹¥¿¥Ã¥¯¤ËÀѤࡣ
   ¼¡¤Ë¥¯¥é¥¤¥¢¥ó¥È¤¬Ì¿Îá SM\_setMathCap ¤òÁ÷¤ë¤È¡¢¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¤ÎºÇ¾å°Ì
   ¤ËÀѤޤì¤Æ¤¤¤ë mathcap ¥ª¥Ö¥¸¥§¥¯¥È¤ò¼è¤ê½Ð¤·¡¢mathcap ¤ÇÀßÄꤵ¤ì¤Æ¤¤¤Ê
   ¤¤¥á¥Ã¥»¡¼¥¸¤ò¥¯¥é¥¤¥¢¥ó¥È¤ØÁ÷¤é¤Ê¤¤¤è¤¦¤ËÀ©¸Â¤ò¹Ô¤¦¡£
   
   ÂèÆó¤Ë¥¯¥é¥¤¥¢¥ó¥È¤òÀ©¸Â¤¹¤ë¤Ë¤Ï¼¡¤Î¤è¤¦¤Ë¤¹¤ë¡£¥¯¥é¥¤¥¢¥ó¥È¤¬¥µ¡¼¥Ð¤ËÌ¿
   Îá SM\_mathcap ¤òÁ÷¤ë¤È¡¢¥µ¡¼¥Ð¤Ï mathcap ¥ª¥Ö¥¸¥§¥¯¥È¤ò¥¹¥¿¥Ã¥¯¤ËÀѤࡣ
   ¤µ¤é¤ËÌ¿Îá SM\_popCMO ¤òÁ÷¤ë¤È¡¢¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¤ÎºÇ¾å°Ì¤Î¥ª¥Ö¥¸¥§¥¯¥È
   (¤¹¤Ê¤ï¤Á mathcap ¥ª¥Ö¥¸¥§¥¯¥È)¤ò¥Ü¥Ç¥£¤È¤¹¤ë¥á¥Ã¥»¡¼¥¸¤ò¥¯¥é¥¤¥¢¥ó¥È¤Ë
   Á÷ÉÕ¤¹¤ë¡£¥¯¥é¥¤¥¢¥ó¥È¤Ï¤½¤Î¥ª¥Ö¥¸¥§¥¯¥È¤ò²òÀϤ·¤Æ¡¢À©¸Â¤ò¤«¤±¤ë¡£
   
   ¼¡¤Ë mathcap ¤Î¥Ç¡¼¥¿¹½Â¤¤Ë¤Ä¤¤¤ÆÀâÌÀ¤¹¤ë¡£
   mathcap ¤Ï CMO ¤Î°ì¼ï¤Ç¤¢¤ë¤Î¤Ç¡¢¤¹¤Ç¤ËÀâÌÀ¤·¤¿¤è¤¦¤Ë \\
   \begin{tabular}{|c|c|} \hline
   ¥Ø¥Ã¥À        & \hspace{10mm} ¥Ü¥Ç¥£ \hspace{10mm} \\ \hline
   \end{tabular} \\
   ¤Î¹½Â¤¤ò»ý¤Á¥Ø¥Ã¥À¤ÎÃÍ¤Ï 5 ¤Ç¤¢¤ë(\ref{sec:cmo} Àá¤ò»²¾È¤Î¤³¤È)¡£
   ¥Ü¥Ç¥£¤Ï cmo\_list ¥ª¥Ö¥¸¥§¥¯¥È¤Ç¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤¡£
   
   %\begin{quote}
   %       cmo\_mathcap := (CMO\_MATHCAP,{\sl cmo} obj)
   %\end{quote}
   
   ¤µ¤Æ¡¢mathcap ¥ª¥Ö¥¸¥§¥¯¥È¤Î¥Ü¥Ç¥£¤Î cmo\_list ¥ª¥Ö¥¸¥§¥¯¥È¤Ï°Ê²¼¤Î¾ò·ï¤ò
   Ëþ¤¿¤¹¤³¤È¤òÍ׵ᤵ¤ì¤ë¡£
   
   ¤Þ¤º¡¢¤½¤Î cmo\_list ¥ª¥Ö¥¸¥§¥¯¥È¤Ï¾¯¤Ê¤¯¤È¤â¥ê¥¹¥ÈŤ¬ 3 °Ê¾å¤Ç¤Ê¤±¤ì¤Ð
   ¤Ê¤é¤Ê¤¤¡£
   
   \begin{quote}
           (CMO\_LIST, {\sl int32} $3$,
                   {\sl cmo} $A$, {\sl cmo} $B$, {\sl cmo} $C$)
   \end{quote}
   %\[     \begin{tabular}{|c|c|c|} \hline
   %       $A$ & $B$ & $C$ \\ \hline
   %       \end{tabular}   \]
   
   Âè°ìÍ×ÁÇ $A$ ¤Ï¤Þ¤¿ cmo\_list ¤Ç¤¢¤ê¡¢¥ê¥¹¥ÈĹ¤Ï 4 °Ê¾å¡¢
   $a_1$ ¤Ï 32 ¥Ó¥Ã¥ÈÀ°¿ô¤Ç¥Ð¡¼¥¸¥ç¥ó¥Ê¥ó¥Ð¡¼¤ò¡¢
   $a_2$, $a_3$, $a_4$ ¤Ïʸ»úÎó¤Ç
   ¤½¤ì¤¾¤ì¥·¥¹¥Æ¥à¤Î̾Á°¡¢¡¢ CPU ¤Î¼ïÎà¤òɽ¤¹¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£
   \begin{quote}
           (CMO\_LIST, {\sl int32} $4$,
                   {\sl cmo\_int32} $a_1$, {\sl cmo\_string} $a_2$,
                   {\sl cmo\_string} $a_3$, {\sl cmo\_string} $a_4$)
   \end{quote}
   
   ÂèÆóÍ×ÁÇ $B$ ¤Ï¼¡¤Î¤è¤¦¤Ê¥ê¥¹¥È¹½Â¤¤ò¤·¤Æ¤¤¤ë¡£
   ¤³¤Î $b_1$, $b_2$, $\cdots$, $b_n$ ¤Ï¤¹¤Ù¤Æ 32 ¥Ó¥Ã¥È¤ÎÀ°¿ô¤Ç¤¢¤ë¡£
   \ref{sec:oxsm} Àá¤Ç¤ß¤¿¤è¤¦¤Ë¡¢
   ¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ø¤ÎÌ¿Îá¤Ï¤¹¤Ù¤Æ 32 ¥Ó¥Ã¥È¤ÎÀ°¿ô¤Çɽ¤·¤Æ¤ª¤ê¡¢
   ³Æ $b_i$ ¤ÏÍøÍѲÄǽ¤ÊÌ¿Îá¤ËÂбþ¤¹¤ë 32 ¥Ó¥Ã¥È¤ÎÀ°¿ô¤È¤Ê¤Ã¤Æ¤¤¤ë¡£
   \begin{quote}
           (CMO\_LIST, {\sl int32} $n$,
                   {\sl cmo\_int32} $b_1$, {\sl cmo\_int32} $b_2$,
                   $\cdots$, {\sl cmo\_int32} $b_n$)
   \end{quote}
   
   Âè»°Í×ÁÇ $C$ ¤Ï°Ê²¼¤Î¤è¤¦¤Ê¥ê¥¹¥È¹½Â¤¤ò¤·¤Æ¤¤¤ë¡£
   \begin{quote}
     (CMO\_LIST, {\sl int32} $m$, \\
     \hspace{10mm} (CMO\_LIST, {\sl int32} $l_1$, {\sl cmo\_int32} $c_{11}$,
                   {\sl cmo} $c_{12}$, $\cdots$, {\sl cmo} $c_{1l_1}$) \\
     \hspace{10mm} (CMO\_LIST, {\sl int32} $l_2$, {\sl cmo\_int32} $c_{21}$,
                   {\sl cmo} $c_{22}$, $\cdots$, {\sl cmo} $c_{1l_2}$) \\
     \hspace{10mm} $\vdots$ \\
     \hspace{10mm} (CMO\_LIST, {\sl int32} $l_m$, {\sl cmo\_int32} $c_{m1}$,
                   {\sl cmo} $c_{m2}$, $\cdots$, {\sl cmo} $c_{1l_m}$))
   \end{quote}
   %%$n$ ¤Ï OX\_COMMAND °Ê³°¤Î¼õ¤±¼è¤ì¤ë¥á¥Ã¥»¡¼¥¸¤Î¥¿¥°¤Î¼ïÎà¤Î¿ô¤ËÅù¤·¤¤¡£
   %%Í×ÁÇ¿ô¤Ï 1 ¤Ç¤â¤â¤Á¤í¤ó¹½¤ï¤Ê¤¤¡£
   ¤É¤Î $c_{i1}$ ¤Ë¤â 32 ¥Ó¥Ã¥È¤ÎÀ°¿ô¤¬Æþ¤Ã¤Æ¤ª¤ê¡¢
   OX\_COMMAND °Ê³°¤Î¡¢¼õ¤±¼è¤ì¤ë¥á¥Ã¥»¡¼¥¸¤Î¥¿¥°¤¬Æþ¤Ã¤Æ¤¤¤ë¡£
   $c_{i2}$ °Ê¹ß¤Ë¤Ä¤¤¤Æ¤ÏºÇ½é¤Î $c_{i1}$ ¤ÎÃͤˤè¤Ã¤Æ¤½¤ì¤¾¤ì°Û¤Ê¤ë¡£
   ¤³¤³¤Ç¤Ï¡¢ºÇ½é¤ÎÍ×ÁǤ¬ OX\_DATA ¤Î¾ì¹ç¤Ë¤Ä¤¤¤Æ¤Î¤ßÀâÌÀ¤¹¤ë¡£
   ¤³¤Î $c_{i1}$ ¤¬ OX\_DATA ¤Î¾ì¹ç¡¢
   $c_{i1}$, $c_{i2}$, $\cdots$, $c_{il_i}$ ¤òÍ×ÁǤȤ¹¤ë cmo\_list ¤Ï
   CMO ·Á¼°¤Ë¤Ä¤¤¤Æ¤Î¾ðÊó¤òɽ¤·¤Æ¤ª¤ê¡¢ $l_i=2$ ¤È·è¤á¤é¤ì¤Æ¤¤¤ë¡£
   $c_{i1}$ ¤Ë¤Ï¤â¤Á¤í¤ó¤Î¤³¤È OX\_DATA ¤¬Æþ¤Ã¤Æ¤ª¤ê¡¢
   $c_{i2}$ ¤Ï°Ê²¼¤Î¿Þ¤Î¤è¤¦¤Ê cmo\_list ¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£
   ³ÆÍ×ÁÇ¤Ï 32 ¥Ó¥Ã¥È¤ÎÀ°¿ô¤Ç¤¢¤ê¡¢
   ¼õ¤±¼è¤ë¤³¤È¤¬²Äǽ¤Ê CMO ·Á¼°¤Î¥¿¥°¤¬Æþ¤ë¡£
   \begin{quote}
           (CMO\_LIST, {\sl int32} $k$,
                   {\sl cmo\_int32} $c_{i21}$, {\sl cmo\_int32} $c_{i22}$,
                           $\cdots$, {\sl cmo\_int32} $c_{i2k}$)
   \end{quote}
   %\[  \overbrace{
   %       \begin{tabular}{|c|c|c|c|c|} \hline
   %       $c_{i21}$ & $c_{i22}$ & $\cdots$ & $c_{i2l}$    \\ \hline
   %       \end{tabular}
   %   }^{c_{i2}}  \]
   
   %¤Ê¤ª¡¢ mathcap ¥Ç¡¼¥¿¤ÎÃæ¤Ç¤Ï CMO ·Á¼°¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë
   %32 bit À°¿ô¡¢Ê¸»úÎ󡢥ꥹ¥È¹½Â¤¤¬»È¤ï¤ì¤Æ¤ª¤ê¡¢
   %mathcap ¥Ç¡¼¥¿¤Ë´Þ¤Þ¤ì¤Æ¤¤¤ëÆâÍƤòÍý²ò¤Ç¤­¤ë¤¿¤á¤Ë¤Ï
   %ɬÁ³Åª¤Ë¤³¤ì¤é¤âÍý²ò¤Ç¤­¤ëɬÍפ¬¤¢¤ë
   %(¤Ã¤Æ¤³¤È¤Ï CMO ·Á¼°¤Î¤È¤³¤í¤Ç¤³¤ì¤é¤ò
   %ÀâÌÀ¤·¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤¤Ã¤Æ¤³¤È¤Ç¤¹)¡£
   
   ¶ñÂÎŪ¤Ê mathcap ¤ÎÎã¤ò¤¢¤²¤è¤¦¡£
   Ì¾Á°¤¬ ``ox\_test''¡¢¥Ð¡¼¥¸¥ç¥ó¥Ê¥ó¥Ð¡¼¤¬ 199911250 ¤Î¥µ¡¼¥Ð¤Ç¡¢
   PC-UNIX ¾å¤ÇÆ°¤¤¤Æ¤¤¤ì¤Ð¡¢
   $A$ ¤ÎÉôʬ¤Ï
   \begin{quote}
   (CMO\_LIST, 4, {\sl cmo\_int32} $199911250$, {\sl cmo\_string} "ox\_test",
           {\sl cmo\_string} "Version=199911250",
           {\sl cmo\_string} "HOSTTYPE=i386")
   \end{quote}
   ¤È¤Ê¤ë¡£
   ¤µ¤é¤Ë¡¢¤³¤Î¥µ¡¼¥Ð¤Î¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤¬
   Ì¿Îᥳ¡¼¥É 2, 3, 5, 7, 11 ÈÖ¤òÍøÍѲÄǽ
   (¼ÂºÝ¤Ë¤Ï¤³¤Î¤è¤¦¤ÊÌ¿Îᥳ¡¼¥É¤Ï¸ºß¤·¤Ê¤¤)¤Ç¤¢¤ì¤Ð¡¢ $B$ ¤ÎÉôʬ¤Ï
   \begin{quote}
           (CMO\_LIST, {\sl int32} $5$,
                   {\sl cmo\_int32} $2$, {\sl cmo\_int32} $3$,
                   {\sl cmo\_int32} $5$, {\sl cmo\_int32} $7$,
                   {\sl cmo\_int32} $11$)
   \end{quote}
   ¤È¤Ê¤ê¡¢
   CMO ·Á¼°¤Î 32 ¥Ó¥Ã¥ÈÀ°¿ô¡¢Ê¸»úÎó¡¢ mathcap ¡¢¥ê¥¹¥È¹½Â¤¤Î¤ß¤¬
   ¼õ¤±¼è¤ì¤ë¤È¤­¤Ë¤Ï¡¢ $C$ ¤ÎÉôʬ¤Ï
   \begin{quote}
     (CMO\_LIST, {\sl int32} $1$, \\
     \ \   (CMO\_LIST, {\sl int32} $4$,
                   {\sl cmo\_int32} $2$, {\sl cmo\_int32} $4$,
                   {\sl cmo\_int32} $5$, {\sl cmo\_int32} $17$))
   \end{quote}
   ¤È¤Ê¤ë¡£
   %CMO\_ZZ ¤¬¤Ê¤¤¤Î¤Ç¡¢¤³¤Î¥µ¡¼¥Ð¤Ï¿ÇÜĹÀ°¿ô¤¬Á÷¤é¤ì¤Æ¤³¤Ê¤¤¤³¤È¤ò
   %´üÂÔ¤·¤Æ¤¤¤ë¡£
   
   %{\Huge ¤Ã¤Æ¤Ê¤ó¤Ç¤Ç¤·¤ç¤¦¤«? ¥Ç¡¼¥¿¤ÎÏÀÍý¹½Â¤¤òÃΤé¤Ê¤¤¤È¼õ¤±¼è¤ì¤Ê¤¤¤È
   %»×¤¦¤ó¤Ç¤¹¤¬$\ldots$}
   
   ¤Ê¤ª¡¢¤³¤Î mathcap ¤Ç¤Ï¡¢¥Ç¡¼¥¿¤ÎÏÀÍý¹½Â¤¤¬Íý²ò¤Ç¤­¤ë¤«¤É¤¦¤«
   ¤Þ¤Ç¤Ïʬ¤«¤é¤Ê¤¤¤Î¤ÇÃí°Õ¤¹¤ëɬÍפ¬¤¢¤ë¡£
   
   
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 \section{¾¤Î¥×¥í¥¸¥§¥¯¥È}  \section{¾¤Î¥×¥í¥¸¥§¥¯¥È}
   
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 OpenMath ¥×¥í¥¸¥§¥¯¥È¤Ï¿ô³ØŪ¤Ê¥ª¥Ö¥¸¥§¥¯¥È¤ò  \begin{itemize}
 ¥³¥ó¥Ô¥å¡¼¥¿¾å¤Çɽ¸½¤¹¤ëÊýË¡¤ò·èÄꤷ¤Æ¤¤¤ë¡£  \item OpenMath\\
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 É½¸½ÊýË¡¤Ï°ì¤Ä¤À¤±¤Ç¤Ê¤¯¡¢ XML ɽ¸½¤ä binary ɽ¸½¤Ê¤É¤¬  ¥È¤ÎÊÑ´¹¼ê½ç¤Ë¤Ä¤Æ¤âÄê¤á¤é¤ì¤Æ¤¤¤ë¡£É½¸½ÊýË¡¤Ï´ö¤Ä¤«¤ÎÃʳ¬¤ÇÄê¤á¤é¤ì¤Æ
 ÍÑ°Õ¤µ¤ì¤Æ¤¤¤ë¡£  ¤¤¤Æ¡¢XML ɽ¸½¤ä¥Ð¥¤¥Ê¥êɽ¸½¤Ê¤É¤¬ÍÑ°Õ¤µ¤ì¤Æ¤¤¤ë¡£¾ÜºÙ¤Ï
 ¾ÜºÙ¤Ï  
   
 http://www.openmath.org/omsoc/index.html A.M.Cohen  http://www.openmath.org/omsoc/   A.M.Cohen
   
   \item NetSolve
   
 °Ê²¼¤Ï½ñ¤¤¤Æ¤ëÅÓÃæ¡£  
   
 NetSolve  
   
 http://www.cs.utk.edu/netsolve/  http://www.cs.utk.edu/netsolve/
   
   \item MP
   
 MP  
   
 http://symbolicNet.mcs.kent.edu/SN/areas/protocols/mp.html  http://symbolicNet.mcs.kent.edu/SN/areas/protocols/mp.html
   
   \item MCP
   
 MCP  
   
 http://horse.mcs.kent.edu/~pwang/  http://horse.mcs.kent.edu/~pwang/
   \end{itemize}
   
   
 \section{¸½ºßÄ󶡤µ¤ì¤Æ¤¤¤ë¥½¥Õ¥È¥¦¥§¥¢}  \section{¸½ºßÄ󶡤µ¤ì¤Æ¤¤¤ë¥½¥Õ¥È¥¦¥§¥¢}
   
 ¸½ºß OpenXM µ¬³Ê¤ËÂбþ¤·¤Æ¤¤¤ë¥¯¥é¥¤¥¢¥ó¥È¤Ë¤Ï  ¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥¯¥é¥¤¥¢¥ó¥È¤Ë¤Ïasir, sm1, Mathematica ¤¬
 asir, sm1, Mathematica ¤¬¤¢¤ë¡£  ¤¢¤ë¡£¤³¤ì¤é¤Î¥¯¥é¥¤¥¢¥ó¥È¤«¤é OpenXM µ¬Ìó¤ËÂбþ¤·¤¿¥µ¡¼¥Ð¤ò¸Æ¤Ó½Ð¤¹¤³¤È
 ¤³¤ì¤é¤Î¥¯¥é¥¤¥¢¥ó¥È¤«¤é  ¤¬¤Ç¤­¤ë¡£¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥µ¡¼¥Ð¥½¥Õ¥È¥¦¥§¥¢¤Ë¤Ï¡¢asir,
 OpenXM µ¬³Ê¤ËÂбþ¤·¤¿¥µ¡¼¥Ð¤ò¸Æ¤Ó½Ð¤¹¤³¤È¤¬¤Ç¤­¤ë¡£  sm1, gnuplot, Mathematica ¤Ê¤É¤¬¤¢¤ê¡¢¤½¤ì¤¾¤ì ox\_asir, ox\_sm1,
 ¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥µ¡¼¥Ð¥½¥Õ¥È¥¦¥§¥¢¤Ë¤Ï¡¢  ox\_sm1\_gnuplot, ox\_math ¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ¤ì¤Æ¤¤¤ë¡£¤Þ¤¿¡¢ OpenMath
  asir, sm1, gnuplot, Mathematica ¤Ê¤É¤¬¤¢¤ê¡¢  µ¬Ìó¤Î XML ɽ¸½¤Çɽ¸½¤µ¤ì¤¿¥ª¥Ö¥¸¥§¥¯¥È¤È CMO ·Á¼°¤Î¥ª¥Ö¥¸¥§¥¯¥È¤òÊÑ´¹¤¹
 ¤½¤ì¤¾¤ì ox\_asir, ox\_sm1, ox\_math ¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ¤ì¤Æ¤¤¤ë¡£  ¤ë¥½¥Õ¥È¥¦¥§¥¢¤¬ JAVA ¤Ë¤è¤Ã¤Æ¼ÂÁõ¤µ¤ì¤Æ¤ª¤ê¡¢OMproxy ¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ
 ¤Þ¤¿¡¢ OpenMath µ¬³Ê¤Î XML ɽ¸½¤Çɽ¸½¤µ¤ì¤¿¥Ç¡¼¥¿¤È CMO ·Á¼°¤Î  ¤ì¤Æ¤¤¤ë¡£
 ¥Ç¡¼¥¿¤òÊÑ´¹¤¹¤ë¥½¥Õ¥È¥¦¥§¥¢¤¬ JAVA ¤Ë¤è¤Ã¤Æ¼ÂÁõ¤µ¤ì¤Æ¤ª¤ê¡¢  
 OMproxy ¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ¤ì¤Æ¤¤¤ë¡£  
   
   \begin{thebibliography}{99}
   \bibitem{Ohara-Takayama-Noro-1999}
   ¾®¸¶¸ùǤ, ¹â»³¿®µ£, ÌîϤÀµ¹Ô:
   {Open asir ÆþÌç}, 1999, ¿ô¼°½èÍý, Vol 7, No 2, 2--17. (ISBN4-87243-086-7, SEG ½ÐÈÇ, Tokyo).
   \bibitem{OpenXM-1999}
   ÌîϤÀµ¹Ô, ¹â»³¿®µ£:
   {Open XM ¤ÎÀ߷פȼÂÁõ --- Open message eXchange protocol for Mathematics},
   1999/11/22
   \end{thebibliography}
   
 \end{document}  \end{document}

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