gcd, gcdz

gcd(poly1,poly2[,mod])

gcdz(poly1,poly2)

:: poly1 ¤È poly2 ¤Î gcd.

return

¿¹à¼°

poly1,poly2

¿¹à¼°

mod

ÁÇ¿ô

• Æó¤Ä¤Î¿¹à¼°¤ÎºÇÂç¸øÌó¼° (GCD) ¤òµá¤á¤ë.
• gcd() ¤ÏÍ­Íý¿ôÂξå¤Î¿¹à¼°¤È¤·¤Æ¤Î GCD ¤òÊÖ¤¹. ¤¹¤Ê¤ï¤Á, ·ë²Ì¤ÏÀ°¿ô·¸¿ô¤Ç, ¤«¤Ä·¸¿ô¤Î GCD ¤¬ 1 ¤Ë¤Ê¤ë¤è¤¦¤Ê¿¹à¼°, ¤Þ¤¿¤Ï, ¸ß¤¤¤ËÁǤξì¹ç¤Ï 1 ¤òÊÖ¤¹.
• gcdz() ¤Ï poly1, poly2 ¤È¤â¤ËÀ°¿ô·¸¿ô¤Î¾ì¹ç¤Ë, À°¿ô´Ä¾å¤Î¿¹à¼°¤È¤·¤Æ¤Î GCD ¤òÊÖ¤¹. ¤¹¤Ê¤ï¤Á, gcd() ¤ÎÃͤË, ·¸¿ôÁ´ÂΤÎÀ°¿ô GCD¤ÎÃͤò³Ý¤±¤¿¤â¤Î¤òÊÖ¤¹.
• °ú¿ô mod ¤¬¤¢¤ë»þ, gcd() ¤Ï GF(mod) ¾å¤Ç¤Î GCD ¤òÊÖ¤¹.
• gcd(), gcdz() Extended Zassenhaus ¥¢¥ë¥´¥ê¥º¥à¤Ë¤è¤ë. Í­¸ÂÂξå¤Î GCD ¤Ï PRS ¥¢¥ë¥´¥ê¥º¥à¤Ë¤è¤Ã¤Æ¤¤¤ë¤¿¤á, Â礭¤ÊÌäÂê, GCD ¤¬ 1 ¤Î¾ì¹ç¤Ê¤É¤Ë¤ª¤¤¤Æ¸úΨ¤¬°­¤¤.

[0] gcd(12*(x^2+2*x+1)^2,18*(x^2+(y+1)*x+y)^3);
x^3+3*x^2+3*x+1
[1] gcdz(12*(x^2+2*x+1)^2,18*(x^2+(y+1)*x+y)^3);
6*x^3+18*x^2+18*x+6
[2] gcd((x+y)*(x-y)^2,(x+y)^2*(x-y));
x^2-y^2
[3] gcd((x+y)*(x-y)^2,(x+y)^2*(x-y),2);
x^3+y*x^2+y^2*x+y^3

»²¾È

section igcd,igcdcntl.

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