ʬ»¶É½¸½Â¿¹à¼°

ʬ»¶É½¸½Â¿¹à¼°¤È¤Ï, ¿¹à¼°¤ÎÆâÉô·Á¼°¤Î°ì¤Ä¤Ç¤¢¤ë. Ä̾ï¤Î¿¹à¼° (type ¤¬ 2) ¤Ï, ºÆµ¢É½¸½¤È¸Æ¤Ð¤ì¤ë·Á¼°¤Çɽ¸½¤µ¤ì¤Æ¤¤¤ë. ¤¹¤Ê¤ï ¤Á, ÆÃÄê¤ÎÊÑ¿ô¤ò¼çÊÑ¿ô¤È¤¹¤ë 1 ÊÑ¿ô¿¹à¼°¤Ç, ¤½¤Î¾¤ÎÊÑ¿ô¤Ï, ¤½¤Î 1 ÊÑ ¿ô¿¹à¼°¤Î·¸¿ô¤Ë, ¼çÊÑ¿ô¤ò´Þ¤Þ¤Ê¤¤Â¿¹à¼°¤È¤·¤Æ¸½¤ì¤ë. ¤³¤Î·¸¿ô¤¬, ¤Þ¤¿, ¤¢¤ëÊÑ¿ô¤ò¼çÊÑ¿ô¤È¤¹¤ë¿¹à¼°¤È¤Ê¤Ã¤Æ¤¤¤ë¤³¤È¤«¤éºÆµ¢É½¸½¤È¸Æ¤Ð¤ì¤ë.

¤³¤ì¤ËÂФ·, ¿¹à¼°¤ò, ÊÑ¿ô¤ÎÑÑÀѤȷ¸¿ô¤ÎÀѤÎϤȤ·¤Æɽ¸½¤·¤¿¤â¤Î¤òʬ»¶ ɽ¸½¤È¸Æ¤Ö.

¥°¥ì¥Ö¥Ê´ðÄì·×»»¤Ë¤ª¤¤¤Æ¤Ï, ñ¹à¼°¤ËÃíÌܤ·¤ÆÁàºî¤ò¹Ô¤¦¤¿¤á¿¹à¼°¤¬Ê¬»¶É½¸½ ¤µ¤ì¤Æ¤¤¤ëÊý¤¬¤è¤ê¸úΨ¤Î¤è¤¤±é»»¤¬²Äǽ¤Ë¤Ê¤ë. ¤³¤Î¤¿¤á, ʬ»¶É½¸½Â¿¹à¼°¤¬, ¼±ÊÌ»Ò 9 ¤Î·¿¤È¤·¤Æ Asir ¤Î¥È¥Ã¥×¥ì¥Ù¥ë¤«¤éÍøÍѲÄǽ¤È¤Ê¤Ã¤Æ¤¤¤ë. ¤³¤³¤Ç, ¸å¤ÎÀâÌÀ¤Î¤¿¤á¤Ë, ¤¤¤¯¤Ä¤«¤Î¸ÀÍÕ¤òÄêµÁ¤·¤Æ¤ª¤¯.

¹à (term)

ÊÑ¿ô¤ÎÑÑÀÑ. ¤¹¤Ê¤ï¤Á, ·¸¿ô 1 ¤Îñ¹à¼°¤Î¤³¤È. Asir ¤Ë¤ª¤¤¤Æ¤Ï,

<<0,1,2,3,4>>

¤È¤¤¤¦·Á¤Çɽ¼¨¤µ¤ì, ¤Þ¤¿, ¤³¤Î·Á¤ÇÆþÎϲÄǽ¤Ç¤¢¤ë. ¤³¤ÎÎã¤Ï, 5 ÊÑ¿ô¤Î¹à ¤ò¼¨¤¹. ³ÆÊÑ¿ô¤ò a, b, c, d, e ¤È¤¹¤ë¤È ¤³¤Î¹à¤Ï b*c^2*d^3*e^4 ¤òɽ¤¹.

¹à½ç½ø (term order)

ʬ»¶É½¸½Â¿¹à¼°¤Ë¤ª¤±¤ë¹à¤Ï, ¼¡¤ÎÀ­¼Á¤òËþ¤¿¤¹Á´½ç½ø¤Ë¤è¤êÀ°Î󤵤ì¤ë.

1. Ǥ°Õ¤Î¹à t ¤ËÂФ· t > 1
2. t, s, u ¤ò¹à¤È¤¹¤ë»þ, t > s ¤Ê¤é¤Ð tu > su

¤³¤ÎÀ­¼Á¤òËþ¤¿¤¹Á´½ç½ø¤ò¹à½ç½ø¤È¸Æ¤Ö. ¤³¤Î½ç½ø¤ÏÊÑ¿ô½ç½ø (ÊÑ¿ô¤Î¥ê¥¹¥È) ¤È¹à½ç½ø·¿ (¿ô, ¥ê¥¹¥È¤Þ¤¿¤Ï¹ÔÎó) ¤Ë¤è¤ê»ØÄꤵ¤ì¤ë.

ñ¹à¼° (monomial)

¹à¤È·¸¿ô¤ÎÀÑ.

2*<<0,1,2,3,4>>

¤È¤¤¤¦·Á¤Çɽ¼¨¤µ¤ì, ¤Þ¤¿, ¤³¤Î·Á¤ÇÆþÎϲÄǽ¤Ç¤¢¤ë.

Ƭñ¹à¼° (head monomial)

Ƭ¹à (head term)

Ƭ·¸¿ô (head coefficient)

ʬ»¶É½¸½Â¿¹à¼°¤Ë¤ª¤±¤ë³Æñ¹à¼°¤Ï, ¹à½ç½ø¤Ë¤è¤êÀ°Î󤵤ì¤ë. ¤³¤Î»þ½ç ½øºÇÂç¤Îñ¹à¼°¤òƬñ¹à¼°, ¤½¤ì¤Ë¸½¤ì¤ë¹à, ·¸¿ô¤ò¤½¤ì¤¾¤ìƬ¹à, Ƭ·¸¿ô ¤È¸Æ¤Ö.

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