det,invmat

det(mat[,mod])

:: mat ¤Î¹ÔÎó¼°¤òµá¤á¤ë.

invmat(mat)

:: mat ¤Î¹ÔÎó¼°¤òµá¤á¤ë.

return

det: ¼°, invmat: ¥ê¥¹¥È

mat

¹ÔÎó

mod

ÁÇ¿ô

• det ¤Ï¹ÔÎó mat ¤Î¹ÔÎó¼°¤òµá¤á¤ë. invmat ¤Ï¹ÔÎó mat ¤ÎµÕ¹ÔÎó¤òµá¤á¤ë. µÕ¹ÔÎó¤Ï [ʬÊì, ʬ»Ò] ¤Î·Á¤ÇÊÖ¤µ¤ì, ʬÊì¤¬¹ÔÎó, ʬÊì/ʬ»Ò ¤¬µÕ¹ÔÎó¤È¤Ê¤ë.
• °ú¿ô mod ¤¬¤¢¤ë»þ, GF(mod) ¾å¤Ç¤Î¹ÔÎó¼°¤òµá¤á¤ë.
• ʬ¿ô¤Ê¤·¤Î¥¬¥¦¥¹¾ÃµîË¡¤Ë¤è¤Ã¤Æ¤¤¤ë¤¿¤á, ¿ÊÑ¿ô¿¹à¼°¤òÀ®Ê¬¤È¤¹¤ë ¹ÔÎó¤ËÂФ·¤Æ¤Ï¾®¹ÔÎó¼°Å¸³«¤Ë¤è¤ëÊýË¡¤Î¤Û¤¦¤¬¸úΨ¤¬¤è¤¤¾ì¹ç¤â¤¢¤ë.

[91] A=newmat(5,5)$                         
[92] V=[x,y,z,u,v];
[x,y,z,u,v]
[93] for(I=0;I<5;I++)for(J=0,B=A[I],W=V[I];J<5;J++)B[J]=W^J;
[94] A;
[ 1 x x^2 x^3 x^4 ]
[ 1 y y^2 y^3 y^4 ]
[ 1 z z^2 z^3 z^4 ]
[ 1 u u^2 u^3 u^4 ]
[ 1 v v^2 v^3 v^4 ]
[95] fctr(det(A));
[[1,1],[u-v,1],[-z+v,1],[-z+u,1],[-y+u,1],[y-v,1],[-y+z,1],[-x+u,1],[-x+z,1],
[-x+v,1],[-x+y,1]]
[96] A = newmat(3,3)$
[97] for(I=0;I<3;I++)for(J=0,B=A[I],W=V[I];J<3;J++)B[J]=W^J;
[98] A;
[ 1 x x^2 ]
[ 1 y y^2 ]
[ 1 z z^2 ]
[99] invmat(A);
[[ -z*y^2+z^2*y z*x^2-z^2*x -y*x^2+y^2*x ]
[ y^2-z^2 -x^2+z^2 x^2-y^2 ]
[ -y+z x-z -x+y ],(-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y]
[100] A*B[0];
[ (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 0 ]
[ 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y 0 ]
[ 0 0 (-y+z)*x^2+(y^2-z^2)*x-z*y^2+z^2*y ]
[101] map(red,A*B[0]/B[1]);
[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 1 ]

»²¾È

section newmat.

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