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- 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¤ÊÑѤÎ
ÀѤò 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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