lex_hensel, lex_tl, tolex, tolex_d, tolex_tl

lex_hensel(plist,vlist1,order,vlist2,homo)

lex_tl(plist,vlist1,order,vlist2,homo)

:: ´ðÄìÊÑ´¹¤Ë¤è¤ë¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì¤Î·×»»

tolex(plist,vlist1,order,vlist2)

tolex_d(plist,vlist1,order,vlist2,procs)

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

:: ¥°¥ì¥Ö¥Ê´ðÄì¤òÆþÎϤȤ¹¤ë, ´ðÄìÊÑ´¹¤Ë¤è¤ë¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì¤Î·×»»

return

¥ê¥¹¥È

plist, vlist1, vlist2, procs

¥ê¥¹¥È

order

¿ô, ¥ê¥¹¥È¤Þ¤¿¤Ï¹ÔÎó

homo

¥Õ¥é¥°

• ɸ½à¥é¥¤¥Ö¥é¥ê¤Î `gr' ¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë.
• lex_hensel(), lex_tl() ¤Ï, ¿¹à¼°¥ê¥¹¥È plist ¤Î, ÊÑ¿ô½ç½ø vlist1, ¹à½ç½ø·¿ order ¤Ë´Ø¤¹¤ë¥°¥ì¥Ö¥Ê´ðÄì¤òµá¤á, ¤½¤ì¤ò, ÊÑ¿ô½ç½ø vlist2 ¤Î¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì¤ËÊÑ´¹¤¹¤ë.
• tolex(), tolex_tl() ¤Ï, ÊÑ¿ô½ç½ø vlist1, ¹à½ç½ø·¿ order ¤Ë´Ø¤¹¤ë¥°¥ì¥Ö¥Ê´ðÄì¤Ç¤¢¤ë ¿¹à¼°¥ê¥¹¥È plist ¤òÊÑ¿ô½ç½ø vlist2 ¤Î¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê ´ðÄì¤ËÊÑ´¹¤¹¤ë. tolex_d() ¤Ï, tolex() ¤Ë¤ª¤±¤ë, ³Æ´ðÄì¤Î·×»»¤ò, »Ò¥×¥í¥»¥¹ ¥ê¥¹¥È procs ¤Î³Æ¥×¥í¥»¥¹¤Ëʬ»¶·×»»¤µ¤»¤ë.
• lex_hensel(), lex_tl() ¤Ë¤ª¤¤¤Æ¤Ï, ¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì¤Î ·×»»¤Ï¼¡¤Î¤è¤¦¤Ë¹Ô¤ï¤ì¤ë. ([Noro,Yokoyama] »²¾È.)
  1. vlist1, order ¤Ë´Ø¤¹¤ë¥°¥ì¥Ö¥Ê´ðÄì G0 ¤ò·×»»¤¹¤ë. (lex_hensel() ¤Î¤ß. )
  2. G0 ¤Î³Æ¸µ¤Î vlist2 ¤Ë´Ø¤¹¤ë¼­½ñ¼°½ç½ø¤Ë¤ª¤±¤ëƬ·¸¿ô¤ò³ä¤é¤Ê¤¤ ¤è¤¦¤ÊÁÇ¿ô p ¤òÁª¤Ó, GF(p) ¾å¤Ç¤Î¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì Gp ¤ò·×»»¤¹¤ë.
  3. Gp ¤Ë¸½¤ì¤ë¤¹¤Ù¤Æ¤Î¹à¤Î, G0 ¤Ë´Ø¤¹¤ëÀµµ¬·Á NF ¤ò·×»»¤¹¤ë.
  4. Gp ¤Î³Æ¸µ f ¤Ë¤Ä¤­, f ¤Î·¸¿ô¤ò̤Äê·¸¿ô¤Ç, f ¤Î³Æ¹à¤òÂбþ¤¹¤ë NF ¤Î¸µ¤ÇÃÖ¤­´¹¤¨, ³Æ¹à¤Î·¸¿ô¤ò 0 ¤ÈÃÖ¤¤¤¿, ̤Äê·¸¿ô¤Ë´Ø¤¹¤ëÀþ·ÁÊýÄø¼°·Ï Lf ¤òºî¤ë.
  5. Lf ¤¬, Ë¡ p ¤Ç°ì°Õ²ò¤ò»ý¤Ä¤³¤È¤òÍѤ¤¤Æ Lf ¤Î²ò¤ò Ë¡ p¤Î²ò¤«¤é Hensel ¹½À®¤Ë¤è¤êµá¤á¤ë.
  6. ¤¹¤Ù¤Æ¤Î Gp ¤Î¸µ¤Ë¤Ä¤­Àþ·ÁÊýÄø¼°¤¬²ò¤±¤¿¤é¤½¤Î²òÁ´ÂΤ¬µá¤á¤ë ¼­½ñ¼°½ç½ø¤Ç¤Î¥°¥ì¥Ö¥Ê´ðÄì. ¤â¤·¤É¤ì¤«¤ÎÀþ·ÁÊýÄø¼°¤Îµá²ò¤Ë¼ºÇÔ¤·¤¿¤é, p ¤ò¤È¤êľ¤·¤Æ¤ä¤êľ¤¹.
• lex_tl(), tolex_tl() ¤Ë¤ª¤¤¤Æ¤Ï, ¼­½ñ¼°½ç½ø¥°¥ì¥Ö¥Ê´ðÄì¤Î ·×»»¤Ï¼¡¤Î¤è¤¦¤Ë¹Ô¤ï¤ì¤ë.
  1. vlist1, order ¤Ë´Ø¤¹¤ë¥°¥ì¥Ö¥Ê´ðÄì G0 ¤ò·×»»¤¹¤ë. (lex_hensel() ¤Î¤ß. )
  2. G0 ¤¬ 0 ¼¡¸µ¥·¥¹¥Æ¥à¤Ç¤Ê¤¤¤È¤­, G0 ¤òÆþÎϤȤ·¤Æ, G0 ¤Î³Æ¸µ¤Î vlist2 ¤Ë´Ø¤¹¤ë¼­½ñ¼°½ç½ø¤Ë¤ª¤±¤ëƬ·¸¿ô¤ò³ä¤é¤Ê¤¤ ¤è¤¦¤ÊÁÇ¿ô p ¤òÁª¤Ó, p ¤òÍѤ¤¤¿ trace-lifting ¤Ë¤è¤ê¼­½ñ¼° ½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¸õÊä¤òµá¤á, ¤â¤·µá¤Þ¤Ã¤¿¤Ê¤é¥Á¥§¥Ã¥¯¤Ê¤·¤Ë¤½¤ì¤¬µá¤á¤ë ¥°¥ì¥Ö¥Ê´ðÄì¤È¤Ê¤ë. ¤â¤·¼ºÇÔ¤·¤¿¤é, p ¤ò¤È¤êľ¤·¤Æ¤ä¤êľ¤¹.
  3. G0 ¤¬ 0 ¼¡¸µ¥·¥¹¥Æ¥à¤Î¤È¤­, G0 ¤òÆþÎϤȤ·¤Æ, ¤Þ¤º, vlist2 ¤ÎºÇ¸å¤ÎÊÑ¿ô°Ê³°¤ò¾Ãµî¤¹¤ë¾Ãµî½ç½ø¤Ë¤è¤ê ¥°¥ì¥Ö¥Ê´ðÄì G1 ¤ò·×»»¤·, ¤½¤ì¤«¤é¼­½ñ¼°½ç½ø¤Î¥°¥ì¥Ö¥Ê´ðÄì¤ò ·×»»¤¹¤ë. ¤½¤ÎºÝ, ³Æ¥¹¥Æ¥Ã¥×¤Ç¤Ï, ÆþÎϤγƸµ¤Î, µá¤á¤ë½ç½ø¤Ë¤ª¤±¤ë Ƭ·¸¿ô¤ò³ä¤é¤Ê¤¤ÁÇ¿ô¤òÍѤ¤¤¿ trace-lifting ¤Ç¥°¥ì¥Ö¥Ê´ðÄì¸õÊä¤òµá¤á, ¤â¤·µá¤Þ¤Ã¤¿¤é¥Á¥§¥Ã¥¯¤Ê¤·¤Ë¤½¤ì¤¬¤½¤Î½ç½ø¤Ç¤Î¥°¥ì¥Ö¥Ê´ðÄì¤È¤Ê¤ë.
• Í­Íý¼°·¸¿ô¤Î·×»»¤Ï, lex_tl(), tolex_tl() ¤Î¤ß¼õ¤±ÉÕ¤±¤ë.
• homo ¤¬ 0 ¤Ç¤Ê¤¤¾ì¹ç, ÆâÉô¤Çµ¯Æ°¤µ¤ì¤ë Buchberger ¥¢¥ë¥´¥ê¥º¥à¤Ë ¤ª¤¤¤Æ, ÀƼ¡²½¤¬¹Ô¤ï¤ì¤ë.
• tolex_d() ¤Çɽ¼¨¤µ¤ì¤ë»þ´Ö¤Ï, ¤³¤ÎÈ¡¿ô¤¬¼Â¹Ô¤µ¤ì¤Æ¤¤¤ë¥×¥í¥»¥¹¤Ë ¤ª¤¤¤Æ¹Ô¤ï¤ì¤¿·×»»¤ËÂбþ¤·¤Æ¤¤¤Æ, »Ò¥×¥í¥»¥¹¤Ë¤ª¤±¤ë»þ´Ö¤Ï´Þ¤Þ¤ì¤Ê¤¤.

[78] K=katsura(5)$ 
30msec + gc : 20msec
[79] V=[u5,u4,u3,u2,u1,u0]$
0msec
[80] G0=hgr(K,V,2)$
91.558sec + gc : 15.583sec
[81] G1=lex_hensel(K,V,0,V,0)$
49.049sec + gc : 9.961sec
[82] G2=lex_tl(K,V,0,V,1)$
31.186sec + gc : 3.500sec
[83] gb_comp(G0,G1);
1
10msec
[84] gb_comp(G0,G2);
1

»²¾È

section dp_gr_main, dp_gr_mod_main, section dp_ord, section ʬ»¶·×»»

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