6.6.7 `det',`invmat'
--------------------

det(MAT[,MOD])
nd_det(MAT[,MOD])
     :: MAT $B$N9TNs<0$r5a$a$k(B.

invmat(MAT)
     :: MAT $B$N5U9TNs$r5a$a$k(B.

RETURN
     `det': $B<0(B, `invmat': $B%j%9%H(B

MAT
     $B9TNs(B

MOD
     $BAG?t(B

   * `det' $B$*$h$S(B `nd_det' $B$O9TNs(B MAT $B$N9TNs<0$r5a$a$k(B.  `invmat'
     $B$O9TNs(B MAT $B$N5U9TNs$r5a$a$k(B. $B5U9TNs$O(B `[$BJ,Jl(B, $BJ,;R(B]' $B$N7A$GJV$5$l(B,
     `$BJ,Jl(B'$B$,9TNs(B, `$BJ,Jl(B/$BJ,;R(B' $B$,5U9TNs$H$J$k(B.

   * $B0z?t(B MOD $B$,$"$k;~(B, GF(MOD) $B>e$G$N9TNs<0$r5a$a$k(B.

   * $BJ,?t$J$7$N%,%&%9>C5nK!$K$h$C$F$$$k$?$a(B, $BB?JQ?tB?9`<0$r@.J,$H$9$k(B
     $B9TNs$KBP$7$F$O>.9TNs<0E83+$K$h$kJ}K!$N$[$&$,8zN($,$h$$>l9g$b$"$k(B.

   * `nd_det' $B$OM-M}?t$^$?$OM-8BBN>e$NB?9`<09TNs$N9TNs<0(B
     $B7W;;@lMQ$G$"$k(B. $B%"%k%4%j%:%`$O$d$O$jJ,?t$J$7$N%,%&%9>C5nK!$@$,(B,
     $B%G!<%?9=B$$*$h$S>h=|;;$N9)IW$K$h$j(B, $B0lHL$K(B `det' $B$h$j9bB.$K(B
     $B7W;;$G$-$k(B.

     [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 ]

$B;2>H(B
     *Note `newmat': newmat.

