̵ʿÊýʬ²ò, °ø¿ôʬ²ò

̵ʿÊýʬ²ò¤Ï, ¿¹à¼°¤È¤½¤ÎÈùʬ¤È¤Î GCD ¤Î·×»»¤«¤é»Ï¤Þ¤ë¤â¤Ã¤È¤â°ìÈÌŪ¤Ê ¥¢¥ë¥´¥ê¥º¥à¤òºÎÍѤ·¤Æ¤¤¤ë. È¡¿ô¤Ï asq() ¤Ç¤¢¤ë.

[116] A=newalg(x^2+x+1);                           
(#4)
[117] T=simpalg((x+A+1)*(x^2-2*A-3)^2*(x^3-x-A)^2);
x^11+(#4+1)*x^10+(-4*#4-8)*x^9+(-10*#4-4)*x^8+(16*#4+20)*x^7+(24*#4-6)*x^6
+(-29*#4-31)*x^5+(-15*#4+28)*x^4+(38*#4+29)*x^3+(#4-23)*x^2+(-21*#4-7)*x
+(3*#4+8)
[118] asq(T);
[[x^5+(-2*#4-4)*x^3+(-#4)*x^2+(2*#4+3)*x+(#4-2),2],[x+(#4+1),1]]

·ë²Ì¤ÏÄ̾ï¤ÈƱÍͤË, [°ø»Ò, ½ÅÊ£ÅÙ] ¤Î¥ê¥¹¥È¤È¤Ê¤ë¤¬, Á´¤Æ¤Î°ø»Ò ¤ÎÀѤÏ, ¤â¤È¤Î¿¹à¼°¤ÈÄê¿ôÇܤκ¹¤Ï¤¢¤êÆÀ¤ë. ¤³¤ì¤Ï, °ø»Ò¤òÀ°¿ô·¸¿ô¤Ë¤· ¤Æ¸«¤ä¤¹¤¯¤¹¤ë¤¿¤á¤Ç, °ø¿ôʬ²ò¤Ç¤âƱÍͤǤ¢¤ë.

Âå¿ôÂξå¤Ç¤Î°ø¿ôʬ²ò¤Ï, Trager ¤Ë¤è¤ë¥Î¥ë¥àË¡¤ò²þÎɤ·¤¿¤â¤Î¤Ç, ÆÃ¤Ë ¤¢¤ë¿¹à¼°¤ËÂФ·, ¤½¤Îº¬¤òź²Ã¤·¤¿Âξå¤Ç¤½¤Î¿¹à¼°¼«¿È¤ò°ø¿ôʬ²ò¤¹¤ë ¾ì¹ç¤ËÆäËÍ­¸ú¤Ç¤¢¤ë.

[119] af(T,[A]);
[[x^3-x+(-#4),2],[x^2+(-2*#4-3),2],[x+(#4+1),1]]

°ú¿ô¤Ï 2 ¤Ä¤Ç, Âè 2 °ú¿ô¤Ï, root ¤Î¥ê¥¹¥È¤Ç¤¢¤ë. °ø¿ôʬ²ò¤Ï Í­Íý¿ôÂΤË, ¤½¤ì¤é¤Î root ¤òź²Ã¤·¤¿Âξå¤Ç¹Ô¤ï¤ì¤ë. root ¤Î½ç½ø¤Ë¤ÏÀ©¸Â¤¬¤¢¤ë. ¤¹¤Ê¤ï¤Á, ¸å¤ÇÄêµÁ¤µ¤ì¤¿¤â¤Î¤Û¤É Á°¤ÎÊý¤Ë¤³¤Ê¤±¤ì¤Ð ¤Ê¤é¤Ê¤¤. ʤٴ¹¤¨¤Ï, ¼«Æ°Åª¤Ë¤Ï¹Ô¤ï¤ì¤Ê¤¤. ¥æ¡¼¥¶¤ÎÀÕǤ¤È¤Ê¤ë.

¥Î¥ë¥à¤òÍѤ¤¤¿°ø¿ôʬ²ò¤Ë¤ª¤¤¤Æ¤Ï, ¥Î¥ë¥à¤Î·×»»¤ÈÀ°¿ô·¸¿ô 1 ÊÑ¿ô¿¹à¼°¤Î °ø¿ôʬ²ò¤Î¸úΨ¤¬, Á´ÂΤθúΨ¤òº¸±¦¤¹¤ë. ¤³¤Î¤¦¤Á, Æä˹⼡¤Î¿¹à¼° ¤Î¾ì¹ç¤Ë¸å¼Ô¤Ë¤ª¤¤¤ÆÁȹ礻Çúȯ¤Ë¤è¤ê·×»»ÉÔǽ¤Ë¤Ê¤ë¾ì¹ç¤¬¤·¤Ð¤·¤ÐÀ¸¤º¤ë.

[120] B=newalg(x^2-2*A-3);
(#5)
[121] af(T,[B,A]);
[[x+(#5),2],[x^3-x+(-#4),2],[x+(-#5),2],[x+(#4+1),1]]

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