fctr, sqfr

fctr(poly)

:: poly ¤ò´ûÌó°ø»Ò¤Ëʬ²ò¤¹¤ë.

sqfr(poly)

:: poly ¤ò̵ʿÊýʬ²ò¤¹¤ë.

return

¥ê¥¹¥È

poly

Í­Íý¿ô·¸¿ô¤Î¿¹à¼°

• Í­Íý¿ô·¸¿ô¤Î¿¹à¼° poly ¤ò°ø¿ôʬ²ò¤¹¤ë. fctr() ¤Ï´ûÌó°ø»Òʬ²ò, sqfr() ¤Ï̵ʿÊý°ø»Òʬ²ò.
• ·ë²Ì¤Ï [[¿ô·¸¿ô,1],[°ø»Ò,½ÅÊ£ÅÙ],...] ¤Ê¤ë¥ê¥¹¥È.
• ¿ô·¸¿ô ¤È Á´¤Æ¤Î °ø»Ò^½ÅÊ£ÅÙ ¤ÎÀѤ¬ poly ¤ÈÅù¤·¤¤.
• ¿ô·¸¿ô ¤Ï, (poly/¿ô·¸¿ô) ¤¬, À°¿ô·¸¿ô¤Ç, ·¸¿ô¤Î GCD ¤¬ 1 ¤È¤Ê¤ë ¤è¤¦¤Ê¿¹à¼°¤Ë¤Ê¤ë¤è¤¦¤ËÁª¤Ð¤ì¤Æ¤¤¤ë. (ptozp() »²¾È)

[0] fctr(x^10-1);
[[1,1],[x-1,1],[x+1,1],[x^4+x^3+x^2+x+1,1],[x^4-x^3+x^2-x+1,1]]
[1] fctr(x^3+y^3+(z/3)^3-x*y*z);
[[1/27,1],[9*x^2+(-9*y-3*z)*x+9*y^2-3*z*y+z^2,1],[3*x+3*y+z,1]]
[2] A=(a+b+c+d)^2;
a^2+(2*b+2*c+2*d)*a+b^2+(2*c+2*d)*b+c^2+2*d*c+d^2
[3] fctr(A);
[[1,1],[a+b+c+d,2]]
[4] A=(x+1)*(x^2-y^2)^2; 
x^5+x^4-2*y^2*x^3-2*y^2*x^2+y^4*x+y^4
[5] sqfr(A);
[[1,1],[x+1,1],[-x^2+y^2,2]]
[6] fctr(A);
[[1,1],[x+1,1],[-x-y,2],[x-y,2]]

»²¾È

section ufctrhint.

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