´ðÄìÊÑ´¹

¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤òµá¤á¤ë¾ì¹ç, ľÀÜ gr() ¤Ê¤É¤òµ¯Æ°¤¹¤ë ¤è¤ê, °ìö¾¤Î½ç½ø (Î㤨¤ÐÁ´¼¡¿ôµÕ¼­½ñ¼°½ç½ø) ¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò·×»»¤·¤Æ, ¤½¤ì¤òÆþÎϤȤ·¤Æ¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò·×»»¤¹¤ëÊý¤¬¸úΨ¤¬¤è¤¤¾ì¹ç ¤¬¤¢¤ë. ¤Þ¤¿, ÆþÎϤ¬²¿¤é¤«¤Î½ç½ø¤Ç¤Î¥°¥ì¥Ö¥Ê´ðÄì¤Ë¤Ê¤Ã¤Æ¤¤¤ë¾ì¹ç, ´ðÄì ÊÑ´¹¤È¸Æ¤Ð¤ì¤ëÊýË¡¤Ë¤è¤ê, Buchberger ¥¢¥ë¥´¥ê¥º¥à¤Ë¤è¤é¤º¤Ë¸úΨÎɤ¯ ¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄ줬·×»»¤Ç¤­¤ë¾ì¹ç¤¬¤¢¤ë. ¤³¤Î¤è¤¦¤ÊÌÜŪ¤Î¤¿¤á¤Î È¡¿ô¤¬, ¥æ¡¼¥¶ÄêµÁÈ¡¿ô¤È¤·¤Æ `gr' ¤Ë¤¤¤¯¤Ä¤«ÄêµÁ¤µ¤ì¤Æ¤¤¤ë. °Ê²¼¤Î 2 ¤Ä¤ÎÈ¡¿ô¤Ï, ÊÑ¿ô½ç½ø vlist1, ¹à½ç½ø·¿ order ¤Ç ´û¤Ë¥°¥ì¥Ö¥Ê´ðÄì¤È¤Ê¤Ã¤Æ¤¤¤ë¿¹à¼°¥ê¥¹¥È gbase ¤ò, ÊÑ¿ô½ç½ø vlist2 ¤Ë¤ª¤±¤ë¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ËÊÑ´¹¤¹¤ëÈ¡¿ô¤Ç¤¢¤ë.

tolex(gbase,vlist1,order,vlist2)

¤³¤ÎÈ¡¿ô¤Ï, gbase ¤¬Í­Íý¿ôÂξå¤Î¥·¥¹¥Æ¥à¤Î¾ì¹ç¤Ë¤Î¤ß»ÈÍѲÄǽ¤Ç¤¢¤ë. ¤³¤ÎÈ¡¿ô¤Ï, ¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò, Í­¸ÂÂξå¤Ç·×»»¤µ¤ì¤¿¥°¥ì¥Ö¥Ê´ðÄì ¤ò¿÷·¿¤È¤·¤Æ, ̤Äê·¸¿ôË¡¤ª¤è¤Ó Hensel ¹½À®¤Ë¤è¤êµá¤á¤ë¤â¤Î¤Ç¤¢¤ë.

tolex_tl(gbase,vlist1,order,vlist2,homo)

¤³¤ÎÈ¡¿ô¤Ï, ¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò Buchberger ¥¢¥ë¥´¥ê¥º¥à¤Ë¤è¤êµá ¤á¤ë¤â¤Î¤Ç¤¢¤ë¤¬, ÆþÎϤ¬¤¢¤ë½ç½ø¤Ë¤ª¤±¤ë¥°¥ì¥Ö¥Ê´ðÄì¤Ç¤¢¤ë¾ì¹ç¤Î trace-lifting¤Ë¤ª¤±¤ë¥°¥ì¥Ö¥Ê´ðÄì¸õÊä¤ÎƬ¹à, Ƭ·¸¿ô¤ÎÀ­¼Á¤òÍøÍѤ·¤Æ, ºÇ½ªÅª¤Ê¥°¥ì¥Ö¥Ê´ðÄì¥Á¥§¥Ã¥¯, ¥¤¥Ç¥¢¥ë¥á¥ó¥Ð¥·¥Ã¥×¥Á¥§¥Ã¥¯¤ò¾Êά¤·¤Æ¤¤ ¤ë¤¿¤á, ñ¤ËBuchberger ¥¢¥ë¥´¥ê¥º¥à¤ò·«¤êÊÖ¤¹¤è¤ê¸úΨ¤è¤¯·×»»¤Ç¤­¤ë. ¹¹¤Ë, ÆþÎϤ¬ 0 ¼¡¸µ¥·¥¹¥Æ¥à¤Î¾ì¹ç, ¼«Æ°Åª¤Ë¤â¤¦ 1 ¤Ä¤ÎÃæ´ÖŪ¤Ê¹à½ç½ø¤ò ·Ðͳ¤·¤Æ¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò·×»»¤¹¤ë. ¿¤¯¤Î¾ì¹ç, ¤³¤ÎÊýË¡¤Ï, ľÀܼ­½ñ¼°½ç½ø¤Î·×»»¤ò¹Ô¤¦¤è¤ê¸úΨ¤¬¤è¤¤. (¤â¤Á¤í¤óÎã³°¤¢¤ê. ) °ú¿ô homo ¤¬ 0 ¤Ç¤Ê¤¤»þ, hgr() ¤ÈƱÍͤËÀƼ¡²½¤ò·Ðͳ¤·¤Æ ·×»»¤ò¹Ô¤¦.

¤½¤Î¾, 0 ¼¡¸µ¥·¥¹¥Æ¥à¤ËÂФ·, Í¿¤¨¤é¤ì¤¿Â¿¹à¼°¤ÎºÇ¾®Â¿¹à¼°¤òµá¤á¤ë È¡¿ô, 0 ¼¡¸µ¥·¥¹¥Æ¥à¤Î²ò¤ò, ¤è¤ê¥³¥ó¥Ñ¥¯¥È¤Ëɽ¸½¤¹¤ë¤¿¤á¤ÎÈ¡¿ô¤Ê¤É¤¬ `gr' ¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë. ¤³¤ì¤é¤Ë¤Ä¤¤¤Æ¤Ï¸Ä¡¹¤ÎÈ¡¿ô¤ÎÀâÌÀ¤ò»²¾È¤Î¤³¤È.

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