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

det(MAT[,MOD])
     :: Determinant of MAT.

invmat(MAT)
     :: Inverse matrix of MAT.

RETURN
     `det': expression, `invmat': list

MAT
     matrix

MOD
     prime

   * `det' computes the determinant of matrix MAT.  `invmat' computes
     the inverse matrix of matrix MAT.  `invmat' returns a list
     `[num,den]', where `num' is a matrix and `num/den' represents the
     inverse matrix.

   * The computation is done over GF(MOD) if MOD is specitied.

   * The fraction free Gaussian algorithm is employed.  For matrices
     with multi-variate polynomial entries, minor expansion algorithm
     sometimes is more efficient than the fraction free Gaussian
     algorithm.

     [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 ]

References
     *Note `newmat': newmat.

