Âå¿ôŪ¿ô¤Îɽ¸½

Asir ¤Ë¤ª¤¤¤Æ¤Ï, Âå¿ôÂΤȤ¤¤¦ÂоݤÏÄêµÁ¤µ¤ì¤Ê¤¤. ÆÈΩ¤·¤¿ÂоݤȤ·¤ÆÄêµÁ¤µ¤ì¤ë¤Î¤Ï, Âå¿ôŪ¿ô¤Ç¤¢¤ë. Âå¿ôÂΤÏ, Í­Íý¿ôÂΤË, Âå¿ôŪ¿ô¤òÍ­¸Â¸Ä ½ç¼¡Åº²Ã¤·¤¿ÂΤȤ·¤Æ²¾ÁÛŪ¤ËÄêµÁ¤µ¤ì¤ë. ¿·¤¿¤ÊÂå¿ôŪ¿ô¤Ï, Í­Íý¿ô¤ª¤è¤Ó ¤³¤ì¤Þ¤ÇÄêµÁ¤µ¤ì¤¿Âå¿ôŪ¿ô¤Î¿¹à¼°¤ò·¸¿ô¤È¤¹¤ë 1 ÊÑ¿ô¿¹à¼° ¤òÄêµÁ¿¹à¼°¤È¤·¤ÆÄêµÁ¤µ¤ì¤ë. °Ê²¼, ¤¢¤ëÄêµÁ¿¹à¼°¤Îº¬¤È¤·¤Æ ÄêµÁ¤µ¤ì¤¿Âå¿ôŪ¿ô¤ò, root ¤È¸Æ¤Ö¤³¤È¤Ë¤¹¤ë.

[0] A0=newalg(x^2+1);
(#0)
[1] A1=newalg(x^3+A0*x+A0);
(#1)
[2]  [type(A0),ntype(A0)];
[1,2]

¤³¤ÎÎã¤Ç¤Ï, A0 ¤Ï x^2+1=0 ¤Îº¬, A1 ¤Ï, ¤½¤Î A0 ¤ò·¸¿ô¤Ë´Þ¤à x^3+A0*x+A0=0 ¤Îº¬¤È¤·¤ÆÄêµÁ¤µ¤ì¤Æ¤¤¤ë.

newalg() ¤Î°ú¿ô¤¹¤Ê¤ï¤ÁÄêµÁ¿¹à¼°¤Ë¤Ï¼¡¤Î¤è¤¦¤ÊÀ©¸Â¤¬¤¢¤ë.

1. ÄêµÁ¿¹à¼°¤Ï 1 ÊÑ¿ô¿¹à¼°¤Ç¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.
2. newalg() ¤Î°ú¿ô¤Ç¤¢¤ëÄêµÁ¿¹à¼°¤Ï, Âå¿ôŪ¿ô¤ò´Þ¤à¼°¤Î´Êñ²½¤Î¤¿ ¤á¤ËÍѤ¤¤é¤ì¤ë. ¤³¤Î´Êñ²½¤Ï, ÁȤ߹þ¤ßÈ¡¿ô srem() ¤ËÁêÅö¤¹¤ëÆâ Éô¥ë¡¼¥Á¥ó¤òÍѤ¤¤Æ¹Ô¤ï¤ì¤ë. ¤³¤Î¤¿¤á, ÄêµÁ¿¹à¼°¤Î¼ç·¸¿ô¤Ï, Í­Íý¿ô¤Ë ¤Ê¤Ã¤Æ¤¤¤ëɬÍפ¬¤¢¤ë.
3. ÄêµÁ¿¹à¼°¤Î·¸¿ô¤Ï ¤¹¤Ç¤ËÄêµÁ¤µ¤ì¤Æ¤¤¤ë root ¤ÎÍ­Íý¿ô·¸¿ô¿¹à¼° ¤Ç¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.
4. ÄêµÁ¿¹à¼°¤Ï, ¤½¤Î·¸¿ô¤Ë´Þ¤Þ¤ì¤ëÁ´¤Æ¤Î root ¤òÍ­Íý¿ô¤Ëź²Ã¤·¤¿ Âξå¤Ç´ûÌó¤Ç¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.

newalg() ¤¬¹Ô¤¦°ú¿ô¥Á¥§¥Ã¥¯¤Ï, 1 ¤ª¤è¤Ó 2 ¤Î¤ß¤Ç¤¢¤ë. ÆäË, °ú¿ô¤ÎÄêµÁ¿¹à¼°¤Î´ûÌóÀ­¤ÏÁ´¤¯¥Á¥§¥Ã¥¯¤µ¤ì¤Ê¤¤. ¤³¤ì¤Ï ´ûÌóÀ­¤Î¥Á¥§¥Ã¥¯¤¬Â¿Âç¤Ê·×»»Î̤òɬÍפȤ¹¤ë¤¿¤á¤Ç, ¤³¤ÎÅÀ¤Ë´Ø¤·¤Æ¤Ï, ¥æ¡¼¥¶¤ÎÀÕǤ¤ËǤ¤µ¤ì¤Æ¤¤¤ë.

°ìö newalg() ¤Ë¤è¤Ã¤ÆÄêµÁ¤µ¤ì¤¿Âå¿ôŪ¿ô¤Ï, ¿ô¤È¤·¤Æ¤Î¼±Ê̻Ҥò»ý¤Á, ¤Þ¤¿, ¿ô¤ÎÃæ¤Ç¤ÏÂå¿ôŪ¿ô¤È¤·¤Æ¤Î¼±Ê̻Ҥò»ý¤Ä. (type(), vtype() »²¾È.) ¤µ¤é¤Ë, Í­Íý¿ô¤È, root ¤ÎÍ­Íý¼°¤âƱÍͤËÂå¿ôŪ¿ô¤È¤Ê¤ë.

[87] N=(A0^2+A1)/(A1^2-A0-1);
((#1+#0^2)/(#1^2-#0-1))
[88] [type(N),ntype(N)];     
[1,2]

Î㤫¤é¤ï¤«¤ë¤è¤¦¤Ë, root¤Ï #n ¤Èɽ¼¨¤µ¤ì¤ë. ¤·¤«¤·, ¥æ¡¼¥¶¤Ï¤³¤Î·Á¤Ç¤ÏÆþÎϤǤ­¤Ê¤¤. root ¤Ï ÊÑ¿ô¤Ë³ÊǼ¤·¤ÆÍѤ¤¤ë¤«, ¤¢¤ë¤¤¤Ï alg(n) ¤Ë¤è¤ê¼è¤ê½Ð¤¹. ¤Þ¤¿, ¸úΨ¤ÏÍî¤Á¤ë¤¬, Á´¤¯Æ±¤¸°ú¿ô (ÊÑ¿ô¤Ï°Û¤Ê¤Ã¤Æ¤¤¤Æ¤â¤è¤¤) ¤Ë¤è¤ê newalg() ¤ò¸Æ¤Ù¤Ð, ¿·¤·¤¤Âå¿ôŪ¿ô¤ÏÄêµÁ¤µ¤ì¤º¤Ë´û¤ËÄêµÁ¤µ¤ì¤¿ ¤â¤Î¤¬ÆÀ¤é¤ì¤ë.

[90] alg(0);
(#0)
[91] newalg(t^2+1);
(#0)

root ¤ÎÄêµÁ¿¹à¼°¤Ï, defpoly() ¤Ë¤è¤ê¼è¤ê½Ð¤»¤ë.

[96] defpoly(A0);     
t#0^2+1
[97] defpoly(A1);
t#1^3+t#0*t#1+t#0

¤³¤³¤Ç¸½¤ì¤¿, t#0, t#1 ¤Ï¤½¤ì¤¾¤ì #0, #1 ¤Ë Âбþ¤¹¤ëÉÔÄ긵¤Ç¤¢¤ë. ¤³¤ì¤é¤â¥æ¡¼¥¶¤¬ÆþÎϤ¹¤ë¤³¤È¤Ï¤Ç¤­¤Ê¤¤. var() ¤Ç¼è¤ê½Ð¤¹¤«, ¤¢¤ë¤¤¤Ï algv(n) ¤Ë¤è¤ê¼è¤ê½Ð¤¹.

[98] var(@);
t#1
[99] algv(0);
t#0
[100] 

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