===================================================================
RCS file: /home/cvs/OpenXM/doc/Attic/genkou19991125.tex,v
retrieving revision 1.93
retrieving revision 1.94
diff -u -p -r1.93 -r1.94
--- OpenXM/doc/Attic/genkou19991125.tex	1999/12/25 17:56:56	1.93
+++ OpenXM/doc/Attic/genkou19991125.tex	1999/12/26 03:55:35	1.94
@@ -1,10 +1,10 @@
 \documentclass{jarticle}
 
-%% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.92 1999/12/25 17:05:28 tam Exp $
+%% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.93 1999/12/25 17:56:56 tam Exp $
 
 \usepackage{jssac}
 
-\title{OpenXM ¤Î¸½¾õ¤Ë¤Ä¤¤¤Æ}
+\title{OpenXM ¥×¥í¥¸¥§¥¯¥È¤Î¸½¾õ¤Ë¤Ä¤¤¤Æ}
 \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}
@@ -56,20 +56,20 @@ OpenXM µ¬Ìó¤Ç¤ÏÄÌ¿®¤ÎÊýË¡¤Ë´ö¤é¤«¤Î¼«Í³ÅÙ¤¬¤¢¤ë¤¬, ¸½º
 
 OpenXM µ¬Ìó¤Çµ¬Äꤵ¤ì¤Æ¤¤¤ë¥á¥Ã¥»¡¼¥¸¤Ï¥Ð¥¤¥È¥¹¥È¥ê¡¼¥à¤È¤Ê¤Ã¤Æ¤ª¤ê, ¼¡
 ¤Î¤è¤¦¤Ê¹½Â¤¤Ë¤Ê¤Ã¤Æ¤¤¤ë.
-
+\begin{center}
 \begin{tabular}{|c|c|}
 \hline
 ¥Ø¥Ã¥À	& \hspace{10mm} ¥Ü¥Ç¥£ \hspace{10mm} \\ 
 \hline
 \end{tabular}
-
+\end{center}
 ¥Ø¥Ã¥À¤ÎŤµ¤Ï 8 ¥Ð¥¤¥È¤Ç¤¢¤ë¤ÈÄê¤á¤é¤ì¤Æ¤¤¤ë.  ¥Ü¥Ç¥£¤ÎŤµ¤Ï¥á¥Ã¥»¡¼¥¸
 ¤´¤È¤Ë°Û¤Ê¤Ã¤Æ¤¤¤ë¤¬, Ťµ¤Ï $0$ ¤Ç¤â¤è¤¤.
 
 ¥Ø¥Ã¥À¤Ï¼¡¤ÎÆó¤Ä¤Î¾ðÊó¤ò»ý¤Ã¤Æ¤¤¤ë.
 \begin{enumerate}
 \item
-Á°È¾¤Î 4 ¥Ð¥¤¥È. ¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤òɽ¤ï¤¹¼±Ê̻ҤǤ¢¤ê, ¥¿¥°¤È¸Æ¤Ð¤ì¤ë.
+Á°È¾¤Î 4 ¥Ð¥¤¥È. ¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤òɽ¤¹¼±Ê̻ҤǤ¢¤ê, ¥¿¥°¤È¸Æ¤Ð¤ì¤ë.
 \item
 ¸åȾ¤Î 4 ¥Ð¥¤¥È. ¥á¥Ã¥»¡¼¥¸¤Ë¤Ä¤±¤é¤ì¤¿Ä̤·ÈÖ¹æ¤Ç¤¢¤ë.
 \end{enumerate}
@@ -210,11 +210,13 @@ Mathematical Object format)¤òÄêµÁ¤·¤Æ¤¤¤ë. ¤³¤Î CMO ·Á
 ¤Æ¤¤¤ë.
 
 CMO ·Á¼°¤Ë¤ª¤±¤ë¥Ç¡¼¥¿¹½Â¤¤Ï¼¡¤Î¤è¤¦¤Ê¹½Â¤¤ò¤â¤Ä.
-
-\begin{tabular}{|c|c|} \hline
-¥Ø¥Ã¥À        & \hspace{10mm} ¥Ü¥Ç¥£ \hspace{10mm} \\ \hline
+\begin{center}
+\begin{tabular}{|c|c|}
+\hline
+¥Ø¥Ã¥À        & \hspace{10mm} ¥Ü¥Ç¥£ \hspace{10mm} \\
+\hline
 \end{tabular}
-
+\end{center}
 ¥Ø¥Ã¥À¤Ï4¥Ð¥¤¥È¤Ç¤¢¤ë. ¥Ü¥Ç¥£¤ÎŤµ¤Ï¤½¤ì¤¾¤ì¤Î¥Ç¡¼¥¿¤Ë¤è¤Ã¤Æ°Û¤Ê¤ë¤¬,
 0¤Ç¤â¤è¤¤.
 
@@ -226,70 +228,63 @@ CMO ¤Ç¤Ï, ¥¿¥°¤Ë¤è¤Ã¤Æ¥Ü¥Ç¥£¤ÎÏÀÍýŪ¹½Â¤¤¬·èÄꤹ¤ë. ¤¹
 ÄêµÁ¤µ¤ì¤Æ¤¤¤ë.
 
 \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_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_ERROR2                         0x7f000002
+#define CMO_NULL                           1
+#define CMO_INT32                          2
+#define CMO_DATUM                          3
+#define CMO_STRING                         4
+#define CMO_MATHCAP                        5
+#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
+#define CMO_BIGFLOAT                       50
+#define CMO_IEEE_DOUBLE_FLOAT              51
+#define CMO_INDETERMINATE                  60
+#define CMO_TREE                           61
+#define CMO_LAMBDA                         62
 \end{verbatim}
 
 ¤³¤ÎÃæ¤Ç CMO\_ERROR2, CMO\_NULL, CMO\_INT32, CMO\_DATUM, CMO\_STRING,
 CMO\_MATHCAP, CMO\_LIST ¤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¤¤.
 
-¤³¤ì¤é¤Ë¤Ä¤¤¤Æ¤Î²òÀâ¤ò¹Ô¤¦Á°¤Ëµ­Ë¡¤Ë¤Ä¤¤¤Æ, ¾¯¤·ÀâÌÀ¤·¤Æ¤ª¤¯.
-¤³¤ÎÏÀʸ¤Ç¤Ï, Âçʸ»ú¤Ç CMO\_INT32 ¤È½ñ¤¤¤¿¾ì¹ç¤Ë¤Ï, ¾åµ­¤ÇÄêµÁ¤·¤¿¼±ÊÌ»Ò
-¤òɽ¤ï¤¹. ¤Þ¤¿ CMO\_INT32 ¤Ç¼±Ê̤µ¤ì¤ë¥ª¥Ö¥¸¥§¥¯¥È¤Î¥¯¥é¥¹(¤¢¤ë¤¤¤Ï¥Ç¡¼
-¥¿¹½Â¤)¤ò cmo\_int32 ¤È¾®Ê¸»ú¤Çɽ¤ï¤¹¤³¤È¤Ë¤¹¤ë.
+¤³¤ì¤é¤Ë¤Ä¤¤¤Æ¤Î²òÀâ¤ò¹Ô¤¦Á°¤Ëµ­Ë¡¤Ë¤Ä¤¤¤Æ, ¾¯¤·ÀâÌÀ¤·¤Æ¤ª¤¯.  ¤³¤ÎÏÀʸ
+¤Ç¤Ï, Âçʸ»ú¤Ç CMO\_INT32 ¤È½ñ¤¤¤¿¾ì¹ç¤Ë¤Ï, ¾åµ­¤ÇÄêµÁ¤·¤¿¼±Ê̻Ҥòɽ¤¹. 
+¤Þ¤¿ CMO\_INT32 ¤Ç¼±Ê̤µ¤ì¤ë¥ª¥Ö¥¸¥§¥¯¥È¤Î¥¯¥é¥¹(¤¢¤ë¤¤¤Ï¥Ç¡¼¥¿¹½Â¤) ¤ò 
+cmo\_int32 ¤È¾®Ê¸»ú¤Çɽ¤¹¤³¤È¤Ë¤¹¤ë.
 
 ¤µ¤Æ cmo ¤òɽ¸½¤¹¤ë¤¿¤á¤Î°ì¤Ä¤Îµ­Ë¡¤òƳÆþ¤¹¤ë. ¤³¤Îµ­Ë¡¤Ï CMO expression
 ¤È¸Æ¤Ð¤ì¤Æ¤¤¤ë. ¤½¤ÎÀµ³Î¤Ê·Á¼°ÅªÄêµÁ¤Ï \cite{OpenXM-1999} ¤ò»²¾È¤¹¤ë¤³¤È.
 
-¤Þ¤º CMO expssion ¤Ï Lisp É÷ɽ¸½¤Î°ì¼ï¤Ç, cmo ¤ò³ç¸Ì¤Ç°Ï¤ó¤À¥ê¥¹¥È¤È¤·
-¤Æɽ¸½¤¹¤ë. ¤½¤ì¤¾¤ì¤ÎÍ×ÁǤϥ«¥ó¥Þ¤Ç¶èÀÚ¤ë.
-Î㤨¤Ð,
+CMO expssion ¤Ï Lisp É÷ɽ¸½¤Î°ì¼ï¤Ç, cmo ¤ò³ç¸Ì¤Ç°Ï¤ó¤À¥ê¥¹¥È¤È¤·¤Æɽ¸½
+¤¹¤ë. ¤½¤ì¤¾¤ì¤ÎÍ×ÁǤϥ«¥ó¥Þ¤Ç¶èÀÚ¤ë.  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.  ¤Ê¤ª, CMO expression ¤Ïñ¤Ê¤ëɽµ­
-Ë¡¤Ç¤¢¤ë¤³¤È¤ËÆäËÃí°Õ¤·¤Æ¤Û¤·¤¤.
+¤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 
+¤Ï¼±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.  ¤Ê¤ª, CMO expression ¤Ïñ¤Ê¤ëɽ
+µ­Ë¡¤Ç¤¢¤ë¤³¤È¤ËÆäËÃí°Õ¤·¤Æ¤Û¤·¤¤.
 
 ¤µ¤Æ, ¤³¤Îµ­Ë¡¤Î¤â¤È¤Ç cmo\_int32 ¤ò¼¡¤Î¥Ç¡¼¥¿¹½Â¤¤Ç¤¢¤ë¤ÈÄêµÁ¤¹¤ë.
 \begin{quote}
@@ -316,7 +311,7 @@ OpenXM µ¬Ìó¤Ç¤Ï, ÄÌ¿®»þ¤ËÍѤ¤¤é¤ì¤ë¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤ò³
 ¤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¤¦.
+¤Þ¤º, 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¥¯¤ËÀѤà.
@@ -347,66 +342,60 @@ cmo\_mathcap := (CMO\_MATHCAP, {\sl cmo\_list})
 
 Âè°ìÍ×ÁÇ $a$ ¤Ï¤Þ¤¿ cmo\_list ¤Ç¤¢¤ê, ¥ê¥¹¥ÈĹ¤Ï 4 °Ê¾å, $a_1$ ¤Ï 
 cmo\_int32 ¤Ç¥Ð¡¼¥¸¥ç¥ó¤òɽ¤¹. $a_2$, $a_3$, $a_4$ ¤Ï cmo\_string ¤Ç¤¢¤ê, 
-¤½¤ì¤¾¤ì¥·¥¹¥Æ¥à¤Î̾Á°, ¥Ð¡¼¥¸¥ç¥ó, HOSTTYPE ¤òɽ¤¹¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë.
+¤½¤ì¤¾¤ì¿ô³Ø¥·¥¹¥Æ¥à¤Î̾Á°, ¥Ð¡¼¥¸¥ç¥ó, HOSTTYPE ¤òɽ¤¹¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë.
 \begin{quote}
 (CMO\_LIST, {\sl int32},
 {\sl cmo\_int32} $a_1$, {\sl cmo\_string} $a_2$, {\sl cmo\_string}
 $a_3$, {\sl cmo\_string} $a_4$, $\ldots$)
 \end{quote}
 
-ÂèÆóÍ×ÁÇ $b$ ¤ÎÉôʬ¤Ï¼¡¤Î¤è¤¦¤Ê¥ê¥¹¥È¹½Â¤¤ò¤·¤Æ¤¤¤ë.
-¤³¤Î $b_1$, $b_2$, $\ldots$, $b_n$ ¤Ï¤¹¤Ù¤Æ cmo\_int32 ¤Ç¤¢¤ë.
-\ref{sec:oxsm} Àá¤ÇÀâÌÀ¤·¤¿¤¬,
-¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ø¤ÎÌ¿Îá¤Ï¤¹¤Ù¤Æ {\sl int32} ¤Çɽ¤µ¤ì¤Æ¤¤¤¿¤³¤È¤ËÃí°Õ¤·¤è
-¤¦. ³Æ $b_i$ ¤ÏÍøÍѲÄǽ¤ÊÌ¿Îá¤ò¥Ü¥Ç¥£¤È¤·¤¿ cmo\_int32 ¤È¤Ê¤Ã¤Æ¤¤¤ë.
+ÂèÆóÍ×ÁÇ $b$ ¤â cmo\_list ¤Ç¤¢¤ê, OpenXM ¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤òÀ©¸æ¤¹¤ë¤¿¤á¤Ë
+ÍѤ¤¤é¤ì¤ë.  ³Æ $b_i$ ¤Ï cmo\_int32 ¤Ç¤¢¤ê, ¥Ü¥Ç¥£¤Ï¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤ÎÌ¿Îá
+¥³¡¼¥É¤Ç¤¢¤ë.  \ref{sec:oxsm} Àá¤ÇÀâÌÀ¤·¤¿¤¬, ¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ø¤ÎÌ¿Îá¤Ï¤¹
+¤Ù¤Æ {\sl int32} ¤Çɽ¤µ¤ì¤Æ¤¤¤¿¤³¤È¤ËÃí°Õ¤·¤è¤¦.
 \begin{quote}
 (CMO\_LIST, {\sl int32} $n$,
-	{\sl cmo\_int32} $b_1$, {\sl cmo\_int32} $b_2$,
-	$\ldots$, {\sl cmo\_int32} $b_n$)
+{\sl cmo\_int32} $b_1$, $\ldots$, {\sl cmo\_int32} $b_n$)
 \end{quote}
 
-Âè»°Í×ÁÇ $c$ ¤Ï°Ê²¼¤Î¤è¤¦¤Ê¥ê¥¹¥È¹½Â¤¤ò¤·¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.
+Âè»°Í×ÁÇ $c$ ¤Ï°Ê²¼¤Î¤è¤¦¤Ê cmo\_list ¤Ç¤¢¤ê, ¥ª¥Ö¥¸¥§¥¯¥È¤ÎÁ÷¼õ¿®¤òÀ©¸æ
+¤¹¤ë¤¿¤á¤ËÍѤ¤¤é¤ì¤ë.  Á÷¼õ¿®¤ÎÀ©¸æ¤Ï¥á¥Ã¥»¡¼¥¸¤Î¼ïÎऴ¤È¤Ë¹Ô¤ï¤ì¤ë.  
 \begin{quote}
-(CMO\_LIST, {\sl int32} $m$,
-	{\sl cmo\_list} $list_1$, {\sl cmo\_list} $list_2$,
-		$\ldots$, {\sl cmo\_list} $list_m$)
+(CMO\_LIST, {\sl int32} $m$, {\sl cmo\_list} $\ell_1$, $\ldots$, 
+{\sl cmo\_list} $\ell_m$)
 \end{quote}
+³Æ $\ell_i$ ¤¬À©¸æ¤Î¤¿¤á¤Î¾ðÊó¤òɽ¤¹.  ¤É¤Î $\ell_i$ ¤â°ì¤Ä°Ê¾å¤ÎÍ×ÁǤò
+»ý¤Ã¤Æ¤ª¤ê, Âè°ìÍ×ÁǤÏɬ¤º cmo\_int32 ¤È¤Ê¤Ã¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.  ¤³¤ì
+¤ÏÀ©¸æ¤¹¤Ù¤­¥á¥Ã¥»¡¼¥¸¤Î¼±Ê̻ҤòÆþ¤ì¤ë¤¿¤á¤Ç¤¢¤ë.
 
-¤É¤Î $list_i$ ¤â 1 ¤Ä°Ê¾å¤ÎÍ×ÁǤò»ý¤Ã¤Æ¤ª¤ê,
-1 ÈÖÌܤÎÍ×ÁǤÏɬ¤º cmo\_int32 ¤È¤Ê¤Ã¤Æ¤¤¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.
-¤³¤ì¤Ï¼õ¤±¼è¤ì¤ë¥ª¥Ö¥¸¥§¥¯¥È¤Î¥á¥Ã¥»¡¼¥¸¤Î¼±Ê̻Ҥò
-Æþ¤ì¤ë¤¿¤á¤Ç¤¢¤ë.
-¤³¤³¤Ç¤Ï, OX\_DATA ¤Î¾ì¹ç¤Ë¤Ä¤¤¤Æ¤Î¤ßÀâÌÀ¤¹¤ë.
-
-1 ÈÖÌܤÎÍ×ÁǤ¬ OX\_DATA ¤Î¾ì¹ç,
-¥ê¥¹¥È $list_i$ ¤Ï°Ê²¼¤Î¤è¤¦¤Ê¹½Â¤¤È¤Ê¤Ã¤Æ¤¤¤ë.
-³Æ $c_{ij}$ ¤Ï cmo\_int32 ¤Ç¤¢¤ê,
-¼õ¤±¼è¤ë¤³¤È¤¬²Äǽ¤Ê CMO ·Á¼°¤Î¥¿¥°¤È¤Ê¤ë.
+³Æ $\ell_i$ ¤Î¹½Â¤¤Ï¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤Ë¤è¤Ã¤Æ°Û¤Ê¤ë.  ¤³¤³¤Ç¤Ï, OX\_DATA 
+¤Î¾ì¹ç¤Ë¤Ä¤¤¤Æ¤Î¤ßÀâÌÀ¤¹¤ë.  Âè°ìÍ×ÁǤ¬ OX\_DATA ¤Î¾ì¹ç, ¥ê¥¹¥È $\ell_i$ 
+¤Ï°Ê²¼¤Î¤è¤¦¤Ê¹½Â¤¤È¤Ê¤Ã¤Æ¤¤¤ë.  ³Æ $c_i$ ¤Ï cmo\_int32 ¤Ç¤¢¤ê, ¤½¤Î¥Ü¥Ç¥£
+¤Ï CMO ¤Î¼±Ê̻ҤǤ¢¤ë.  $c_i$ ¤Ç»Ø¼¨¤µ¤ì¤¿ CMO ¤Î¤ß¤¬Á÷¼õ¿®¤¹¤ë¤³¤È¤òµö
+¤µ¤ì¤ë.
 \begin{quote}
 (CMO\_LIST, 2, (CMO\_INT32, OX\_DATA), \\
-\ \ 	(CMO\_LIST, {\sl int32} $k$,
-		{\sl cmo\_int32} $c_{i1}$, {\sl cmo\_int32} $c_{i2}$,
-			$\ldots$, {\sl cmo\_int32} $c_{ik}$))
+\ \ (CMO\_LIST, {\sl int32} $k$, {\sl cmo\_int32} $c_1$, 
+$\ldots$, {\sl cmo\_int32} $c_k$))
 \end{quote}
 
 ¶ñÂÎŪ¤Ê mathcap ¤ÎÎã¤ò¤¢¤²¤è¤¦.  ̾Á°¤¬ ``ox\_test'', ¥Ð¡¼¥¸¥ç¥ó¥Ê¥ó¥Ð¡¼
-¤¬ 199911250 ¤Î¥µ¡¼¥Ð¤Ç, PC-UNIX ¾å¤ÇÆ°¤¤¤Æ¤ª¤ê,
-¤³¤Î¥µ¡¼¥Ð¤Î¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤¬Ì¿Îá SM\_popCMO, SM\_popString,
-SM\_mathcap, SM\_executeStringByLocalParser ¤òÍøÍѲÄǽ,
-¤«¤Ä cmo\_int32, cmo\_string, cmo\_mathcap, cmo\_list ¤Î¤ß¤ËÀ©¸Â¤·¤¿¤¤
-¤È¤­¤Î mathcap ¤Ï
+¤¬ 199911250 ¤Î¥µ¡¼¥Ð¤Ç, Linux ¾å¤ÇÆ°¤¤¤Æ¤ª¤ê, ¤³¤Î¥µ¡¼¥Ð¤Î¥¹¥¿¥Ã¥¯¥Þ¥·
+¥ó¤¬Ì¿Îá SM\_popCMO, SM\_popString, SM\_mathcap,
+SM\_executeStringByLocalParser ¤òÍøÍѲÄǽ¤Ç, ¤«¤Ä ¥ª¥Ö¥¸¥§¥¯¥È¤ò 
+cmo\_int32, cmo\_string, cmo\_mathcap, cmo\_list ¤Î¤ß¤ËÀ©¸Â¤·¤¿¤¤¤È¤­¤Î 
+mathcap ¤Ï
 \begin{quote}
 (CMO\_LIST, 3, \\
-\ \ (CMO\_LIST, 4, (CMO\_INT32, $199911250$), (CMO\_STRING, 7, "ox\_test"), \\
-\ \ \ \ 	(CMO\_STRING, 9, "199911250"), (CMO\_STRING, 4, "i386")) \\
-\ \ (CMO\_LIST, $5$, (CMO\_INT32, SM\_popCMO), \\
-\ \ \ \ 	(CMO\_INT32, SM\_popString), (CMO\_INT32, SM\_mathcap), \\
-\ \ \ \ 	(CMO\_INT32, SM\_executeStringByLocalParser)) \\
-\ \ (CMO\_LIST, $1$, \\
-\ \ \ \ (CMO\_LIST, $2$, (CMO\_INT32, OX\_DATA), \\
-\ \ \ \ \ \ (CMO\_LIST, $4$, (CMO\_INT32, CMO\_INT32), \\
-\ \ \ \ \ \ \ \ (CMO\_INT32, CMO\_STRING), (CMO\_INT32, CMO\_MATHCAP), \\
-\ \ \ \ \ \ \ \ (CMO\_INT32, CMO\_LIST)))))
+$\quad$ (CMO\_LIST, 4, (CMO\_INT32, $199911250$), (CMO\_STRING, 7, ``ox\_test''), \\
+$\qquad$ (CMO\_STRING, 9, ``199911250''), (CMO\_STRING, 4, ``i386'')) \\
+$\quad$ (CMO\_LIST, $5$, (CMO\_INT32, SM\_popCMO), \\
+$\qquad$ (CMO\_INT32, SM\_popString), (CMO\_INT32, SM\_mathcap), \\
+$\qquad$ (CMO\_INT32, SM\_executeStringByLocalParser)) \\
+$\quad$ (CMO\_LIST, $1$, (CMO\_LIST, $2$, (CMO\_INT32, OX\_DATA), \\
+$\qquad$ (CMO\_LIST, $4$, (CMO\_INT32, CMO\_INT32), \\
+$\qquad\quad$ (CMO\_INT32, CMO\_STRING), (CMO\_INT32, CMO\_MATHCAP), \\
+$\qquad\quad$ (CMO\_INT32, CMO\_LIST)))))
 \end{quote}
 ¤Ë¤Ê¤ë.
 
@@ -433,9 +422,10 @@ OpenXM µ¬Ìó¤Ï TCP/IP ¤òÍѤ¤¤ÆÄÌ¿®¤ò¹Ô¤¦¤³¤È¤ò¹Íθ¤·¤Æ¤
 ssh ¤òÍøÍѤ·¤ÆÂбþ¤·¤Æ¤¤¤ë.
 
 
-\section{¾¤Î¥×¥í¥¸¥§¥¯¥È}
+\section{OpenXM °Ê³°¤Î¥×¥í¥¸¥§¥¯¥È}
 
-¾¤Î¥×¥í¥¸¥§¥¯¥È¤Ë¤Ä¤¤¤Æ¤â¿¨¤ì¤Æ¤ª¤³¤¦.
+OpenXM °Ê³°¤Ë¤â¿ô¼°½èÍý¥·¥¹¥Æ¥à´Ö¤ÎÄÌ¿®¤òÌܻؤ·¤¿¥×¥í¥¸¥§¥¯¥È¤Ï¸ºß¤¹¤ë. 
+¤³¤³¤Ç¤Ï¾¤Î¥×¥í¥¸¥§¥¯¥È¤Ë¤Ä¤¤¤Æ¤â¿¨¤ì¤Æ¤ª¤³¤¦.
 
 \begin{itemize}
 \item ESPRIT OpenMath Project
@@ -445,10 +435,11 @@ http://www.openmath.org/omsoc/
 ¿ô³ØŪÂоݤΠSGML Ūɽµ­¤Îɸ½à²½¤òÌܻؤ·¤¿Â絬ÌÏ¤Ê¥×¥í¥¸¥§¥¯¥È. °Û¤Ê¤ë¼ï
 Îà¤Î¿ô¼°½èÍý¥·¥¹¥Æ¥à¤Î´Ö¤Ç¾ðÊó¤ò¸ò´¹¤¹¤ë¤È¤­¤Ë, OpenMath ¤ÇÄêµÁ¤µ¤ì¤¿É½
 ¸½¤òÍøÍѤ¹¤ë¤³¤È¤¬¤Ç¤­¤ë.  ¼ÂºÝ¤Î¾ðÊó¸ò´¹¤Î¼ê³¤­¤Ë¤Ï¤¤¤í¤¤¤í¤Ê¤â¤Î¤¬¹Í
-¤¨¤é¤ì¤ë¤¬, Î㤨¤Ð MCP (Mathematical Computation Protocol) ¤Ê¤ë¼ê³¤­¤¬
-¹Í°Æ¤µ¤ì¤Æ¤¤¤ë.  MCP ¤Ë¤è¤Ã¤ÆÁ÷¿®¤µ¤ì¤ë¥Ç¡¼¥¿¤Ï, ËÜʸ¤Ë OpenMath ·Á¼°¤Ç
-¿ô¼°¤òµ­½Ò¤·¤¿¥Æ¥­¥¹¥È¤Ç, ¤¤¤µ¤µ¤«¥á¥¤¥ë¤Ë»÷¤Æ¤¤¤Ê¤¯¤â¤Ê¤¤.  ¼ÂºÝ¤Ë¤³¤Î
-ÊýË¡¤Ç GAP ¤È Axiom ¤Î´Ö¤ÇÄÌ¿®¤¬¹Ô¤ï¤ì¤Æ¤¤¤ë.
+¤¨¤é¤ì¤ë¤¬, Î㤨¤Ð MCP (Mathematical Computation Protocol) ¤Ë¤è¤Ã¤ÆÄÌ¿®
+¤ò¹Ô¤¦¤³¤È¤¬¤Ç¤­¤ë.
+MCP ¤Ë¤è¤Ã¤ÆÁ÷¿®¤µ¤ì¤ë¥Ç¡¼¥¿¤Ï, ËÜʸ¤Ë OpenMath ·Á¼°¤Ç¿ô¼°¤òµ­½Ò¤·¤¿¥Æ¥­
+¥¹¥È¤Ç, ¤¤¤µ¤µ¤«¥á¥¤¥ë¤Ë»÷¤Æ¤¤¤Ê¤¯¤â¤Ê¤¤.
+¼ÂºÝ¤Ë¤³¤ÎÊýË¡¤Ç GAP ¤È Axiom ¤Î´Ö¤ÇÄÌ¿®¤¬¹Ô¤ï¤ì¤Æ¤¤¤ë.
 
 \item NetSolve
 
@@ -463,40 +454,35 @@ NetSolve ¤Ï¥¯¥é¥¤¥¢¥ó¥È¡¦¥µ¡¼¥Ð·¿¤Îʬ»¶¥·¥¹¥Æ¥à¤Ç¤¢¤ê,
 
 \item MP
 
-http://symbolicNet.mcs.kent.edu/SN/areas/protocols/mp.html
+http://symbolicnet.mcs.kent.edu/SN/areas/protocols/mp.html
 
-²Ê³Øµ»½Ñ·×»»¤ò¹Ô¤Ê¤¦¥½¥Õ¥È¥¦¥§¥¢´Ö¤Ç¿ô³ØŪ¤Ê¥Ç¡¼¥¿¤ò¸úΨŪ¤Ë¸ò´¹
-¤µ¤»¤ë¤³¤È¤òÌÜŪ¤È¤·¤¿¥×¥í¥È¥³¥ë¤òºîÀ®¤·¤Æ¤¤¤ë. ÌÚ¹½Â¤¤òÍѤ¤¤Æ
-´Êñ, ¤«¤Ä½ÀÆð¤Ê¤â¤Î¤òÌܻؤ·¤Æ¤ª¤ê, ¥Ç¡¼¥¿¤Îɽ¸½ÊýË¡¤ä¸ò´¹ÊýË¡¤Ë
-Éé¤ï¤º¤Ë¥½¥Õ¥È¥¦¥§¥¢¤òºî¤ë¤³¤È¤¬¤Ç¤­¤ë¤è¤¦¤Ë¤·¤è¤¦¤È¤·¤Æ¤¤¤ë.
-¸½ºß¤¹¤Ç¤Ë, C ¸À¸ì¤ÇÍøÍѲÄǽ¤Ê¥é¥¤¥Ö¥é¥ê¤¬Ä󶡤µ¤ì¤Æ¤¤¤ë.
+²Ê³Øµ»½Ñ·×»»¤ò¹Ô¤Ê¤¦¥½¥Õ¥È¥¦¥§¥¢´Ö¤Ç¿ô³ØŪ¤Ê¥Ç¡¼¥¿¤ò¸úΨŪ¤Ë¸ò´¹¤µ¤»¤ë¤³
+¤È¤òÌÜŪ¤È¤·¤¿¥×¥í¥È¥³¥ë¤òºîÀ®¤·¤Æ¤¤¤ë. ÌÚ¹½Â¤¤òÍѤ¤¤Æ, ´Êñ¤«¤Ä½ÀÆð¤Ê¤â
+¤Î¤òÌܻؤ·¤Æ¤ª¤ê, ¥Ç¡¼¥¿¤Îɽ¸½ÊýË¡¤ä¸ò´¹ÊýË¡¤Ë¤è¤é¤º¤Ë¥½¥Õ¥È¥¦¥§¥¢¤òºî¤ë
+¤³¤È¤¬¤Ç¤­¤ë¤è¤¦¤Ë¤¹¤ë¤Î¤¬ÌÜɸ¤Ç¤¢¤ë.  ¸½ºß¤¹¤Ç¤Ë, C ¸À¸ì¤ÇÍøÍѲÄǽ¤Ê¥é
+¥¤¥Ö¥é¥ê¤¬Ä󶡤µ¤ì¤Æ¤¤¤ë.
 
 \item MCP
 
 http://horse.mcs.kent.edu/\~{}pwang/
 
-¿ô³ØŪ¤Ê·×»»¤ò¹Ô¤Ê¤¦¤¿¤á¤Î HTTP ¥¹¥¿¥¤¥ë¤Î¥×¥í¥È¥³¥ë.
-¥¯¥é¥¤¥¢¥ó¥È¡¦¥µ¡¼¥Ð¥â¥Ç¥ë¤òºÎÍѤ·¤Æ¤ª¤ê,
-¥Ô¥¢¥Ä¡¼¥Ô¥¢¤Î¥¹¥È¥ê¡¼¥à¥³¥Í¥¯¥·¥ç¥ó¤ò¹Ô¤Ê¤¦.
-¿ô³ØŪ¤Ê¥ª¥Ö¥¸¥§¥¯¥È¤ò MP ¤ä MathML ¤ÇÄê¤á¤é¤ì¤¿ÊýË¡¤Ç
-ɽ¸½¤¹¤ë¤³¤È¤¬¹Í¤¨¤é¤ì¤Æ¤¤¤ë.
-¤¹¤Ç¤Ë OpenMath ¤òÍѤ¤¤¿¼ÂÁõ¤¬Â¸ºß¤¹¤ë.
-
-
+¿ô³ØŪ¤Ê·×»»¤ò¹Ô¤Ê¤¦¤¿¤á¤Î HTTP ¥¹¥¿¥¤¥ë¤Î¥×¥í¥È¥³¥ë.  ¥¯¥é¥¤¥¢¥ó¥È¡¦¥µ¡¼
+¥Ð¥â¥Ç¥ë¤òºÎÍѤ·¤Æ¤ª¤ê, ¥Ô¥¢¥Ä¡¼¥Ô¥¢¤Î¥¹¥È¥ê¡¼¥à¥³¥Í¥¯¥·¥ç¥ó¤ò¹Ô¤Ê¤¦. 
+¿ô³ØŪ¤Ê¥ª¥Ö¥¸¥§¥¯¥È¤ò MP ¤ä MathML ¤ÇÄê¤á¤é¤ì¤¿ÊýË¡¤Çɽ¸½¤¹¤ë¤³¤È¤¬¹Í¤¨
+¤é¤ì¤Æ¤¤¤ë.  ¤¹¤Ç¤Ë OpenMath ¤òÍѤ¤¤¿¼ÂÁõ¤¬Â¸ºß¤¹¤ë.
 \end{itemize}
 
 
 \section{¸½ºßÄ󶡤µ¤ì¤Æ¤¤¤ë¥½¥Õ¥È¥¦¥§¥¢}
 
-¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥¯¥é¥¤¥¢¥ó¥È¤Ë¤Ïasir, sm1, Mathematica ¤¬¤¢¤ë.
-¤³¤ì¤é¤Î¥¯¥é¥¤¥¢¥ó¥È¤«¤é OpenXM µ¬Ìó¤ËÂбþ¤·¤¿¥µ¡¼¥Ð¤ò¸Æ¤Ó½Ð¤¹¤³¤È
-¤¬¤Ç¤­¤ë. ¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥µ¡¼¥Ð¥½¥Õ¥È¥¦¥§¥¢¤Ë¤Ï, asir,
-sm1, gnuplot, Mathematica, PHC pack ¤Ê¤É¤¬¤¢¤ê,
-¤½¤ì¤¾¤ì ox\_asir, ox\_sm1, ox\_sm1\_gnuplot, ox\_math, ox\_sm1\_phc
-¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ¤ì¤Æ¤¤¤ë. ¤Þ¤¿, OpenMath
-µ¬Ìó¤Î XML ɽ¸½¤Çɽ¸½¤µ¤ì¤¿¥ª¥Ö¥¸¥§¥¯¥È¤È CMO ·Á¼°¤Î¥ª¥Ö¥¸¥§¥¯¥È¤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.
+¸½ºß OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥¯¥é¥¤¥¢¥ó¥È¤Ë¤Ïasir, sm1, Mathematica ¤¬
+¤¢¤ë.  ¤³¤ì¤é¤Î¥¯¥é¥¤¥¢¥ó¥È¤«¤é OpenXM µ¬Ìó¤ËÂбþ¤·¤¿¥µ¡¼¥Ð¤ò¸Æ¤Ó½Ð¤¹¤³
+¤È¤¬¤Ç¤­¤ë.  ¤Þ¤¿ OpenXM µ¬Ìó¤ËÂбþ¤·¤Æ¤¤¤ë¥µ¡¼¥Ð¤Ë¤Ï, asir, sm1,
+Mathematica, gnuplot, PHC pack ¤Ê¤É¤¬¤¢¤ê, ¤½¤ì¤¾¤ì ox\_asir, ox\_sm1,
+ox\_math, ox\_sm1\_gnuplot, ox\_sm1\_phc ¤È¤¤¤¦Ì¾Á°¤ÇÄ󶡤µ¤ì¤Æ¤¤¤ë. 
+¤µ¤é¤Ë OpenMath µ¬Ìó¤Î XML ɽ¸½¤Çɽ¸½¤µ¤ì¤¿¥ª¥Ö¥¸¥§¥¯¥È¤È CMO ·Á¼°¤Î¥ª¥Ö
+¥¸¥§¥¯¥È¤òÁê¸ßÊÑ´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}