asq, af, af_noalg

asq(poly)

:: Âå¿ôÂξå¤Î 1 ÊÑ¿ô¿¹à¼°¤Î̵ʿÊýʬ²ò

af(poly,alglist)

af_noalg(poly,defpolylist)

:: Âå¿ôÂξå¤Î 1 ÊÑ¿ô¿¹à¼°¤Î°ø¿ôʬ²ò

return

¥ê¥¹¥È

poly

¿¹à¼°

alglist

root ¤Î¥ê¥¹¥È

defpolylist

root ¤òɽ¤¹ÉÔÄ긵¤ÈÄêµÁ¿¹à¼°¤Î¥Ú¥¢¤Î¥ê¥¹¥È

• ¤¤¤º¤ì¤â `sp' ¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤ë.
• root ¤ò´Þ¤Þ¤Ê¤¤¾ì¹ç¤ÏÀ°¿ô¾å¤ÎÈ¡¿ô¤¬¸Æ¤Ó½Ð¤µ¤ì¹â®¤Ç¤¢¤ë¤¬, root ¤ò´Þ¤à¾ì¹ç¤Ë¤Ï, cr_gcda() ¤¬µ¯Æ°¤µ¤ì¤ë¤¿¤á¤·¤Ð¤·¤Ð »þ´Ö¤¬¤«¤«¤ë.
• af() ¤Ï, ´ðÁÃÂΤλØÄê, ¤¹¤Ê¤ï¤ÁÂè 2 °ú¿ô¤Î, root ¤Î¥ê¥¹¥È ¤Î»ØÄ꤬ɬÍפǤ¢¤ë.
• alglist ¤Ç»ØÄꤵ¤ì¤ë root ¤Ï, ¸å¤ÇÄêµÁ¤µ¤ì¤¿¤â¤Î¤Û¤ÉÁ°¤Î Êý¤ËÍè¤Ê¤±¤ì¤Ð¤Ê¤é¤Ê¤¤.
• af(F,AL) ¤Ë¤ª¤¤¤Æ, AL ¤ÏÂå¿ôŪ¿ô¤Î¥ê¥¹¥È¤Ç¤¢¤ê, Í­Íý¿ôÂΤΠÂå¿ô³ÈÂç¤òɽ¤¹. AL=[An,...,A1] ¤È½ñ¤¯¤È¤­, ³Æ Ak ¤Ï, ¤½¤ì¤è¤ê ±¦¤Ë¤¢¤ëÂå¿ôŪ¿ô¤ò·¸¿ô¤È¤·¤¿, ¥â¥Ë¥Ã¥¯¤ÊÄêµÁ¿¹à¼°¤ÇÄêµÁ¤µ¤ì¤Æ¤¤¤Ê¤±¤ì¤Ð ¤Ê¤é¤Ê¤¤.

  [1] A1 = newalg(x^2+1);
  [2] A2 = newalg(x^2+A1);
  [3] A3 = newalg(x^2+A2*x+A1);
  [4] af(x^2+A2*x+A1,[A2,A1]);
  [[x^2+(#1)*x+(#0),1]]
  

  af_noalg ¤Ç¤Ï, poly ¤Ë´Þ¤Þ¤ì¤ëÂå¿ôŪ¿ô ai ¤òÉÔÄ긵 vi ¤ÇÃÖ¤­´¹¤¨¤ë. defpolylist ¤Ï, [[vn,dn(vn,...,v1)],...,[v1,d(v1)]] ¤Ê¤ë¥ê¥¹¥È¤Ç¤¢¤ë. ¤³¤³¤Ç di(vi,...,v1) ¤Ï ai ¤ÎÄêµÁ¿¹à¼°¤Ë¤ª¤¤¤Æ Âå¿ôŪ¿ô¤òÁ´¤Æ vj ¤ËÃÖ¤­´¹¤¨¤¿¤â¤Î¤Ç¤¢¤ë.

  [1] af_noalg(x^2+a2*x+a1,[[a2,a2^2+a1],[a1,a1^2+1]]);
  [[x^2+a2*x+a1,1]]
  

• ·ë²Ì¤Ï, Ä̾ï¤Î̵ʿÊýʬ²ò, °ø¿ôʬ²ò¤ÈƱÍÍ [°ø»Ò, ½ÅÊ£ÅÙ] ¤Î¥ê¥¹¥È¤Ç¤¢¤ë. af_noalg ¤Î¾ì¹ç, °ø»Ò ¤Ë¸½¤ì¤ëÂå¿ôŪ¿ô¤Ï, defpolylist ¤Ë½¾¤Ã¤ÆÉÔÄ긵¤ËÃÖ¤­´¹¤¨¤é¤ì¤ë.
• ½ÅÊ£ÅÙ¤ò¹þ¤á¤¿°ø»Ò¤ÎÁ´¤Æ¤ÎÀѤÏ, poly ¤ÈÄê¿ôÇܤΰ㤤¤¬¤¢¤êÆÀ¤ë.

[98] A = newalg(t^2-2);
(#0)
[99] asq(-x^4+6*x^3+(2*alg(0)-9)*x^2+(-6*alg(0))*x-2);
[[-x^2+3*x+(#0),2]]
[100] af(-x^2+3*x+alg(0),[alg(0)]);
[[x+(#0-1),1],[-x+(#0+2),1]]
[101] af_noalg(-x^2+3*x+a,[[a,x^2-2]]);
[[x+a-1,1],[-x+a+2,1]]

»²¾È

section cr_gcda, section fctr, sqfr

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