´ðËÜŪ¤ÊÈ¡¿ô

`gr' ¤Ç¤Ï¿ô¿¤¯¤ÎÈ¡¿ô¤¬ÄêµÁ¤µ¤ì¤Æ¤¤¤ë¤¬, ľÀÜ ¥°¥ì¥Ö¥Ê´ðÄì¤ò·×»»¤¹¤ë¤¿¤á¤Î¥È¥Ã¥×¥ì¥Ù¥ë¤Ï¼¡¤Î 3 ¤Ä¤Ç¤¢¤ë. °Ê²¼¤Ç, plist ¤Ï¿¹à¼°¤Î¥ê¥¹¥È, vlist ¤ÏÊÑ¿ô (ÉÔÄ긵) ¤Î¥ê¥¹¥È, order ¤ÏÊÑ¿ô½ç½ø·¿, p ¤Ï 2^27 ̤Ëþ¤ÎÁÇ¿ô¤Ç¤¢¤ë.

gr(plist,vlist,order)

Gebauer-Moeller ¤Ë¤è¤ë useless pair elimination criteria, sugar strategy ¤ª¤è¤Ó Traverso ¤Ë¤è¤ë trace-lifting ¤òÍѤ¤¤¿ Buchberger ¥¢¥ë ¥´¥ê¥º¥à¤Ë¤è¤ëÍ­Íý¿ô·¸¿ô¥°¥ì¥Ö¥Ê´ðÄì·×»»È¡¿ô. °ìÈ̤ˤϤ³¤ÎÈ¡¿ô¤òÍѤ¤¤ë.

hgr(plist,vlist,order)

ÆþÎÏ¿¹à¼°¤òÀƼ¡²½¤·¤¿¸å gr() ¤Î¥°¥ì¥Ö¥Ê´ðÄì¸õÊäÀ¸À®Éô¤Ë¤è¤ê¸õ ÊäÀ¸À®¤·, ÈóÀƼ¡²½, interreduce ¤·¤¿¤â¤Î¤ò gr() ¤Î¥°¥ì¥Ö¥Ê´ðÄì ¥Á¥§¥Ã¥¯Éô¤Ç¥Á¥§¥Ã¥¯¤¹¤ë. 0 ¼¡¸µ¥·¥¹¥Æ¥à (²ò¤Î¸Ä¿ô¤¬Í­¸Â¸Ä¤ÎÊýÄø¼°·Ï) ¤Î¾ì¹ç, sugar strategy ¤¬·¸¿ôËÄÄ¥¤ò°ú¤­µ¯¤³¤¹¾ì¹ç¤¬¤¢¤ë. ¤³¤Î¤è¤¦¤Ê¾ì ¹ç, strategy ¤òÀƼ¡²½¤Ë¤è¤ë strategy ¤ËÃÖ¤­´¹¤¨¤ë¤³¤È¤Ë¤è¤ê·¸¿ôËÄÄ¥¤ò ÍÞÀ©¤¹¤ë¤³¤È¤¬¤Ç¤­¤ë¾ì¹ç¤¬Â¿¤¤.

gr_mod(plist,vlist,order,p)

Gebauer-Moeller ¤Ë¤è¤ë useless pair elimination criteria, sugar strategy ¤ª¤è¤Ó Buchberger ¥¢¥ë¥´¥ê¥º¥à¤Ë¤è¤ë GF(p) ·¸¿ô¥°¥ì¥Ö¥Ê´ðÄì·× »»È¡¿ô.

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