===================================================================
RCS file: /home/cvs/OpenXM/doc/Attic/genkou19991125.tex,v
retrieving revision 1.72
retrieving revision 1.73
diff -u -p -r1.72 -r1.73
--- OpenXM/doc/Attic/genkou19991125.tex	1999/12/24 12:03:33	1.72
+++ OpenXM/doc/Attic/genkou19991125.tex	1999/12/24 15:42:24	1.73
@@ -1,11 +1,13 @@
 \documentclass{jarticle}
 
-%% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.71 1999/12/24 11:16:45 tam Exp $
+%% $OpenXM: OpenXM/doc/genkou19991125.tex,v 1.72 1999/12/24 12:03:33 tam Exp $
 
 \usepackage{jssac}
 \title{
 1. °ÕÌ£¤â¤Ê¤¤½¤¾þ²á¾ê¤Ê¸ì¶ç¤ÏÇÓ½ü¤·¤Þ¤·¤ç¤¦¡£\\
-3. ¤»¤Ã¤«¤¯ fill ¤·¤Æ¤¤¤ë¤Î¤ò¤¤¤¸¤é¤Ê¤¤¤Ç¤¯¤ì¡£
+3. ¤»¤Ã¤«¤¯ fill ¤·¤Æ¤¤¤ë¤Î¤ò¤¤¤¸¤é¤Ê¤¤¤Ç¤¯¤ì¡£\\
+4. Åļ¤¬Í·¤ó¤Ç¤Ð¤«¤ê¤Ç¤ª¤ì¤Ð¤«¤ê»Å»ö¤ò¤·¤Æ¤¤¤ë¤Î¤Ï¤É¤¦¹Í¤¨¤Æ¤âÉÔ¸øÊ¿¤À¡£
+¤Ê¤ó¤Ç»Å»ö¤ò¤·¤Ê¤¤¤Î¤«¡¢¤¤¤¤²Ã¸º»Å»ö¤ò¤·¤í¡¢Åļ¡£
 }
 
 \author{±ü ë ¡¡ ¹Ô ±û\affil{¿À¸ÍÂç³ØÂç³Ø±¡¼«Á³²Ê³Ø¸¦µæ²Ê}
@@ -112,7 +114,8 @@ OpenXM µ¬Ìó¤Ç¤Î·×»»¤È¤Ï¥á¥Ã¥»¡¼¥¸¤ò¸ò´¹¤¹¤ë¤³¤È¤Ç¤¢¤ë¡
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-¤Ç¤¢¤ë¤³¤È¤Ç¼Â¸½¤µ¤ì¤ë¡£¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Î¹½Â¤¤Ë¤Ä¤¤¤Æ¤Ï ?? Àá¤Ç½Ò¤Ù¤ë¡£
+¤Ç¤¢¤ë¤³¤È¤Ç¼Â¸½¤µ¤ì¤ë¡£¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Î¹½Â¤¤Ë¤Ä¤¤¤Æ¤Ï \ref{sec:oxsm} Àá
+¤Ç½Ò¤Ù¤ë¡£
 
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 ¥á¥Ã¥»¡¼¥¸¤Î¥Ü¥Ç¥£)¤Ï¤¹¤Ù¤Æ¥¹¥¿¥Ã¥¯¤ËÀѤޤì¤ë¡£¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ø¤ÎÌ¿Îá
@@ -144,7 +147,7 @@ OpenXM µ¬Ìó¤Ç¤Î·×»»¤È¤Ï¥á¥Ã¥»¡¼¥¸¤ò¸ò´¹¤¹¤ë¤³¤È¤Ç¤¢¤ë¡
 Á÷½Ð¤¹¤ë¡£
 \end{enumerate}
 
-\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 
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@@ -198,7 +201,7 @@ OpenXM µ¬Ìó¤Ç¤Ï¥µ¡¼¥Ð¤Ï¥¹¥¿¥Ã¥¯¥Þ¥·¥ó¤Ç¤¢¤ë¤ÈÄêµÁ¤·¤Æ¤
 ɬÍפǤ¢¤í¤¦¡£
 
 
-\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
 Mathematical Object format)¤òÄêµÁ¤·¤Æ¤¤¤ë¡£¤³¤Î CMO ·Á¼°¤Ë¤·¤¿¤¬¤Ã¤¿¥Ç¡¼
@@ -211,95 +214,146 @@ CMO ·Á¼°¤Ë¤ª¤±¤ë¥Ç¡¼¥¿¹½Â¤¤Ï¼¡¤Î¤è¤¦¤Ê¹½Â¤¤ò¤â¤Ä¡£
 ¥Ø¥Ã¥À        & \hspace{10mm} ¥Ü¥Ç¥£ \hspace{10mm} \\ \hline
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+¥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¤¤¡£
 
-%¤³¤³¤Ç¤Ï CMO ·Á¼°¤ÎÃæ¤Ç¤â¤è¤¯»È¤ï¤ì¤ë¤â¤Î¤Î¤ß¤Ë¤Ä¤¤¤ÆÀâÌÀ¤¹¤ë¡£
+¥á¥Ã¥»¡¼¥¸¤ÈƱÍͤ˥إåÀ¤Ï4¥Ð¥¤¥Èñ°Ì¤Ë´ÉÍý¤µ¤ì¤ë¡£¤¹¤Ê¤ï¤Á¡¢CMO ¤Ç¤Ï¥Ø¥Ã
+¥À¤Ï°ì¤Ä¤À¤±¤Î¾ðÊó¤ò´Þ¤à¡£¤³¤Î4¥Ð¥¤¥È¤Î¥Ø¥Ã¥À¤Î¤³¤È¤ò¥¿¥°¤È¤â¤¤¤¦¡£¤µ¤Æ¡¢
+CMO ¤Ç¤Ï¡¢¥¿¥°¤Ë¤è¤Ã¤Æ¥Ü¥Ç¥£¤ÎÏÀÍýŪ¹½Â¤¤¬·èÄꤹ¤ë¡£¤¹¤Ê¤ï¤Á¡¢¥¿¥°¤Ï¤½¤ì
+¤¾¤ì¤Î¥Ç¡¼¥¿¹½Â¤¤È1ÂÐ1¤ËÂбþ¤¹¤ë¼±Ê̻ҤǤ¢¤ë¡£¤½¤ì¤¾¤ì¤ÎÏÀÍýŪ¹½Â¤¤Ï 
+\cite{OpenXM-1999} ¤Ë¾Ü½Ò¤µ¤ì¤Æ¤¤¤ë¡£¸½ºß¤Î OpenXM µ¬Ìó¤Ç¤Ï°Ê²¼¤Î CMO ¤¬
+ÄêµÁ¤µ¤ì¤Æ¤¤¤ë¡£
 
-¥Ø¥Ã¥À¤ÎÉôʬ¤Ë¤¢¤ë(¥á¥Ã¥»¡¼¥¸¤Î¼±Ê̻ҤȤÏÊ̤ˤ¢¤ë)¥¿¥°¤ò¸«¤ì¤Ð¡¢
-¤É¤Î¤è¤¦¤Ê¥Ç¡¼¥¿¤Ç¤¢¤ë¤Î¤«È½Ê̤Ǥ­¤ë¤è¤¦¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£
-¤³¤ì¤Ï¥á¥Ã¥»¡¼¥¸¤Î¼ïÎà¤ÎȽÊ̤λÅÊý¤È¤ª¤Ê¤¸¤Ç¤¢¤ë¡£
-¤Ê¤ª¡¢¥¿¥°¤Ï³Æ¥Ç¡¼¥¿Ëè¤Ë 32 bit ¤ÎÀ°¿ô¤Çɽ¤µ¤ì¤Æ¤¤¤ë¡£
-¤è¤¯»È¤ï¤ì¤ë¤È»×¤ï¤ì¤ë CMO ·Á¼°¤Î¥¿¥°¤ò¤¢¤²¤Æ¤ª¤¯¡£
 \begin{verbatim}
-#define CMO_INT32    2 /* (CMO ·Á¼°¤Î)32 ¥Ó¥Ã¥ÈÀ°¿ô */
-#define CMO_STRING   4 /* ʸ»úÎó                    */
-#define CMO_MATHCAP  5 /* mathcap(¸å½Ò)             */
-#define CMO_LIST    17 /* ¥ê¥¹¥È¹½Â¤                */
-#define CMO_ZZ      20 /* ¿ÇÜĹÀ°¿ô                */
+#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_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}
-¥¿¥°°Ê¹ß¤Ï¥Ç¡¼¥¿ËÜÂΤǤ¢¤ê¡¢¥Ç¡¼¥¿ËÜÂΤι½Â¤¤Ï¥Ç¡¼¥¿¤Î¼ïÎà¤Ë¤è¤Ã¤Æ°Û¤Ê¤ë¡£
-CMO ·Á¼°¤ÎÀ°¿ôÃÍ $123456789$ ¤òɽ¤¹ CMO\_INT32 ¤Ï
 
-\begin{tabular}{|c|c|} \hline
-CMO\_INT32 & $123456789$	\\ \hline
-\end{tabular}
+¤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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-¤³¤Îɽµ­Êý¤ò CMO expression ¤È¤¤¤¦¡£
-ƱÍͤˡ¢Ä¹¤µ 6 ¤Îʸ»úÎó {\tt ``OpenXM''} ¤ò CMO\_STRING ¤Çɽ¤¹¤È¡¢
-(CMO\_STRING, 6, ``OpenXM'') ¤È¤Ê¤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±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¡£
 
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-OpenXM µ¬Ìó¤Ç¤Ï¥Ð¥¤¥È¥¹¥È¥ê¡¼¥à¤Ç 32 bit ¤ÎÀ°¿ô 20 ¤ò
-{\tt 00 00 00 14} ¤Èɽ¤¹ÊýË¡¤È {\tt 14 00 00 00} ¤Èɽ¤¹ÊýË¡¤¬¤¢¤ë¡£
-¤³¤Îɽ¸½ÊýË¡¤Î°ã¤¤¤Ï¥¯¥é¥¤¥¢¥ó¥È¤È¥µ¡¼¥Ð¤ÎºÇ½é¤ÎÀܳ»þ¤Ë
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+¤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¡£
 
-Àè¤Û¤É¤Î¡¢ (CMO\_INT32, 123456789) ¤ò¥Í¥Ã¥È¥ï¡¼¥¯¥Ð¥¤¥È¥ª¡¼¥À¡¼¤Ç
-¥Ð¥¤¥ÈÎó¤Ëľ¤¹¤È¡¢
-\begin{center}
-	{\tt 00 00 00 02 07 5b cd 15}
-\end{center}
-¤È¤Ê¤ê¡¢
-(CMO\_STRING, 6, ``OpenXM'') ¤Ï
-\begin{center}
-	{\tt 00 00 00 04 00 00 00 06 4f 70 65 6e 58 4d}
-\end{center}
-¤È¤Ê¤ë¡£
+¤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¶èÀڤ롣
+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¡£
 
+¤µ¤Æ¡¢¤³¤Îµ­Ë¡¤Î¤â¤È¤Ç cmo\_int32 ¤ò¼¡¤Î¥Ç¡¼¥¿¹½Â¤¤ò»ý¤Ä¤ÈÄêµÁ¤¹¤ë¡£
+\begin{quote}
+cmo\_int32 := (CMO\_INT32,  {\sl int32})
+\end{quote}
 
-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¡£
+{\Huge ƱÍÍ¤Ë cmo\_string, cmo\_list ¤Ê¤É¤òÄêµÁ!!}
 
-\begin{tabular}{|c|c|c|c|c|} \hline
-$f$ & $b_0$ & $b_1$ & $\cdots$ & $b_{n-1}$ \\ \hline
-\end{tabular}
+% ¤³¤³¤Ç 32 bit ¤ÎÀ°¿ô¤Îɽ¸½ÊýË¡¤Ë¤Ä¤¤¤Æ¿¨¤ì¤Æ¤ª¤¯¡£
+% OpenXM µ¬Ìó¤Ç¤Ï¥Ð¥¤¥È¥¹¥È¥ê¡¼¥à¤Ç 32 bit ¤ÎÀ°¿ô 20 ¤ò
+% {\tt 00 00 00 14} ¤Èɽ¤¹ÊýË¡¤È {\tt 14 00 00 00} ¤Èɽ¤¹ÊýË¡¤¬¤¢¤ë¡£
+% ¤³¤Îɽ¸½ÊýË¡¤Î°ã¤¤¤Ï¥¯¥é¥¤¥¢¥ó¥È¤È¥µ¡¼¥Ð¤ÎºÇ½é¤ÎÀܳ»þ¤Ë
+% ÁÐÊý¤Î¹ç°Õ¤Ç·èÄꤹ¤ë¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£
+% ¤Ê¤ª¡¢¹ç°Õ¤¬¤Ê¤¤¾ì¹ç¤Ë¤ÏÁ°¼Ô¤Îɽ¸½ÊýË¡
+% (°Ê¸å¡¢¤³¤Îɽ¸½ÊýË¡¤ò¥Í¥Ã¥È¥ï¡¼¥¯¥Ð¥¤¥È¥ª¡¼¥À¡¼¤È¸Æ¤Ö)¤ò
+% »È¤¦¤³¤È¤Ë¤Ê¤Ã¤Æ¤¤¤ë¡£
+% ¤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¡£
 
-¤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¡£
+% Àè¤Û¤É¤Î¡¢ (CMO\_INT32, 123456789) ¤ò¥Í¥Ã¥È¥ï¡¼¥¯¥Ð¥¤¥È¥ª¡¼¥À¡¼¤Ç
+% ¥Ð¥¤¥ÈÎó¤Ëľ¤¹¤È¡¢
+% \begin{center}
+% 	{\tt 00 00 00 02 07 5b cd 15}
+% \end{center}
+% ¤È¤Ê¤ê¡¢
+% (CMO\_STRING, 6, ``OpenXM'') ¤Ï
+% \begin{center}
+% 	{\tt 00 00 00 04 00 00 00 06 4f 70 65 6e 58 4d}
+% \end{center}
+% ¤È¤Ê¤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}
-	{\tt 00 00 00 14 00 00 00 02 00 00 00 02 00 00 00 01}
-\end{center}
-¤È¤Ê¤ë¡£¤Þ¤¿¡¢Æ±¤¸É½¸½ÊýË¡¤Ç $-1$ ¤òɽ¸½¤¹¤ë¤È¡¢
-\begin{center}
-	{\tt 00 00 00 14 ff ff ff ff 00 00 00 01}
-\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¡£
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