sp, sp_noalg

sp(poly)

sp_noalg(poly)

:: ºÇ¾®Ê¬²òÂΤòµá¤á¤ë.

return

¥ê¥¹¥È

poly

¿¹à¼°

• `sp' ¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë.
• Í­Íý¿ô·¸¿ô¤Î 1 ÊÑ¿ô¿¹à¼° poly ¤ÎºÇ¾®Ê¬²òÂÎ, ¤ª¤è¤Ó¤½¤ÎÂξå¤Ç¤Î poly ¤Î 1 ¼¡°ø»Ò¤Ø¤Îʬ²ò¤òµá¤á¤ë.
• ·ë²Ì¤Ï, poly ¤Î°ø»Ò¤Î¥ê¥¹¥È¤È, ºÇ¾®Ê¬²òÂΤÎ, Ã༡³ÈÂç¤Ë¤è¤ëɽ¸½ ¤«¤é¤Ê¤ë¥ê¥¹¥È¤Ç¤¢¤ë. sp_noalg ¤Ç¤Ï, Á´¤Æ¤ÎÂå¿ôŪ¿ô¤¬, Âбþ¤¹¤ë ÉÔÄ긵 (¨¤Á #i ¤ËÂФ¹¤ë t#i) ¤ËÃÖ¤­´¹¤¨¤é¤ì¤ë. ¤³¤ì¤Ë ¤è¤ê, sp_noalg ¤Î½ÐÎϤÏ, À°¿ô·¸¿ô¿ÊÑ¿ô¿¹à¼°¤Î¥ê¥¹¥È¤È¤Ê¤ë.
• ºÇ¾®Ê¬²òÂΤÏ, [root,algptorat(defpoly(root))] ¤Î¥ê¥¹¥È¤È¤·¤Æ ɽ¸½¤µ¤ì¤Æ¤¤¤ë. ¤¹¤Ê¤ï¤Á, µá¤á¤ëºÇ¾®Ê¬²òÂΤÏ, Í­Íý¿ôÂΤË, ¤³¤Î root ¤òÁ´¤Æź²Ã¤·¤¿ÂΤȤ·¤ÆÆÀ¤é¤ì¤ë. ź²Ã¤Ï, ±¦¤ÎÊý¤Î root ¤«¤é½ç¤Ë ¹Ô¤ï¤ì¤ë.
• sp() ¤Ï, ÆâÉô¤Ç¥Î¥ë¥à¤Î·×»»¤Î¤¿¤á¤Ë sp_norm() ¤ò¤·¤Ð¤·¤Ð µ¯Æ°¤¹¤ë. ¥Î¥ë¥à¤Î·×»»¤Ï, ¾õ¶·¤Ë±þ¤¸¤Æ¤µ¤Þ¤¶¤Þ¤ÊÊýË¡¤Ç¹Ô¤ï¤ì¤ë¤¬, ¤½¤³¤ÇÍѤ¤¤é¤ì¤ëÊýË¡¤¬ºÇÁ±¤È¤Ï¸Â¤é¤º, ñ½ã¤Ê½ª·ë¼°¤Î·×»»¤ÎÊý¤¬¹â® ¤Ç¤¢¤ë¾ì¹ç¤â¤¢¤ë. Âç°èÊÑ¿ô USE_RES ¤ò 1 ¤ËÀßÄꤹ¤ë¤³¤È¤Ë¤è¤ê, ¾ï¤Ë½ª·ë¼°¤Ë¤è¤ê·×»» ¤µ¤»¤ë¤³¤È¤¬¤Ç¤­¤ë.

[101] L=sp(x^9-54);
[[x+(-#2),-54*x+(#1^6*#2^4),54*x+(#1^6*#2^4+54*#2),54*x+(-#1^8*#2^2),
-54*x+(#1^5*#2^5),54*x+(#1^5*#2^5+#1^8*#2^2),-54*x+(-#1^7*#2^3-54*#1),
54*x+(-#1^7*#2^3),x+(-#1)],[[(#2),t#2^6+t#1^3*t#2^3+t#1^6],[(#1),t#1^9-54]]]
[102] for(I=0,M=1;I<9;I++)M*=L[0][I];
[111] M=simpalg(M);
-1338925209984*x^9+72301961339136
[112] ptozp(M);
-x^9+54

»²¾È

section asq, af, af_noalg, section defpoly, section algptorat, section sp_norm.

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