sdiv, sdivm, srem, sremm, sqr, sqrm

sdiv(poly1,poly2[,v])

sdivm(poly1,poly2,mod[,v])

:: poly1 ¤ò poly2 ¤Ç³ä¤ë½ü»»¤¬ºÇ¸å¤Þ¤Ç¼Â¹Ô¤Ç¤­¤ë¾ì¹ç¤Ë¾¦¤òµá¤á¤ë.

srem(poly1,poly2[,v])

sremm(poly1,poly2,mod[,v])

:: poly1 ¤ò poly2 ¤Ç³ä¤ë½ü»»¤¬ºÇ¸å¤Þ¤Ç¼Â¹Ô¤Ç¤­¤ë¾ì¹ç¤Ë¾ê;¤òµá¤á¤ë.

sqr(poly1,poly2[,v])

sqrm(poly1,poly2,mod[,v])

:: poly1 ¤ò poly2 ¤Ç³ä¤ë½ü»»¤¬ºÇ¸å¤Þ¤Ç¼Â¹Ô¤Ç¤­¤ë¾ì¹ç¤Ë¾¦, ¾ê;¤ò µá¤á¤ë.

return

sdiv(), sdivm(), srem(), sremm() : ¿¹à¼°, sqr(), sqrm() : [¾¦,¾ê;] ¤Ê¤ë¥ê¥¹¥È

poly1 poly2

¿¹à¼°

v

ÉÔÄ긵

mod

ÁÇ¿ô

• poly1 ¤ò poly2 ¤Î¼çÊÑ¿ô var(poly2) ( °ú¿ô v ¤¬¤¢¤ë¾ì¹ç¤Ë¤Ï v) ¤Ë´Ø¤¹¤ë¿¹à¼°¤È¸«¤Æ, poly2 ¤Ç, ³ä¤ê»»¤ò¹Ô¤¦.
• sdivm(), sremm(), sqrm() ¤Ï GF(mod) ¾å¤Ç·×»»¤¹¤ë.
• ¿¹à¼°¤Î½ü»»¤Ï, ¼ç·¸¿ô¤É¤¦¤·¤Î³ä»»¤Ë¤è¤êÆÀ¤é¤ì¤¿¾¦¤È, ¼çÊÑ¿ô¤ÎŬÅö¤ÊÑѤΠÀѤò poly2 ¤Ë³Ý¤±¤Æ, poly1 ¤«¤é°ú¤¯¤È¤¤¤¦Áàºî¤ò poly1 ¤Î¼¡¿ô¤¬ poly2 ¤Î¼¡¿ô¤è¤ê¾®¤µ¤¯¤Ê¤ë¤Þ¤Ç·«¤êÊÖ¤·¤Æ ¹Ô¤¦. ¤³¤ÎÁàºî¤¬, ¿¹à¼°¤ÎÈÏ°ÏÆâ¤Ç¹Ô¤ï¤ì¤ë¤¿¤á¤Ë¤Ï, ³Æ¥¹¥Æ¥Ã¥×¤Ë¤ª¤¤¤Æ ¼ç·¸¿ô¤É¤¦¤·¤Î½ü»»¤¬, ¿¹à¼°¤È¤·¤Æ¤ÎÀ°½ü¤Ç¤¢¤ëɬÍפ¬¤¢¤ë. ¤³¤ì¤¬, ¡Ö½ü»» ¤¬ºÇ¸å¤Þ¤Ç¼Â¹Ô¤Ç¤­¤ë¡×¤³¤È¤Î°ÕÌ£¤Ç¤¢¤ë.
• ŵ·¿Åª¤Ê¾ì¹ç¤È¤·¤Æ, poly2 ¤Î¼ç·¸¿ô¤¬, Í­Íý¿ô¤Ç¤¢¤ë¾ì¹ç, ¤¢¤ë¤¤¤Ï, poly2 ¤¬ poly1 ¤Î°ø»Ò¤Ç¤¢¤ë¤³¤È¤¬¤ï¤«¤Ã¤Æ¤¤¤ë¾ì¹ç¤Ê¤É ¤¬¤¢¤ë.
• sqr() ¤Ï¾¦¤È¾ê;¤òƱ»þ¤Ëµá¤á¤¿¤¤»þ¤ËÍѤ¤¤ë.
• À°¿ô½ü»»¤Î¾¦, ¾ê;¤Ï idiv, irem ¤òÍѤ¤¤ë.
• ·¸¿ô¤ËÂФ¹¤ë¾ê;±é»»¤Ï % ¤òÍѤ¤¤ë.

[0] sdiv((x+y+z)^3,x^2+y+a);    
x+3*y+3*z
[1] srem((x+y+z)^2,x^2+y+a);
(2*y+2*z)*x+y^2+(2*z-1)*y+z^2-a
[2] X=(x+y+z)*(x-y-z)^2;
x^3+(-y-z)*x^2+(-y^2-2*z*y-z^2)*x+y^3+3*z*y^2+3*z^2*y+z^3
[3] Y=(x+y+z)^2*(x-y-z);  
x^3+(y+z)*x^2+(-y^2-2*z*y-z^2)*x-y^3-3*z*y^2-3*z^2*y-z^3
[4] G=gcd(X,Y);
x^2-y^2-2*z*y-z^2
[5] sqr(X,G);
[x-y-z,0]
[6] sqr(Y,G);
[x+y+z,0]
[7] sdiv(y*x^3+x+1,y*x+1);  
divsp: cannot happen
return to toplevel

»²¾È

section idiv, irem, section %.

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