`katsura', `hkatsura', `cyclic', `hcyclic'
------------------------------------------

katsura(N)

hkatsura(N)

cyclic(N)

hcyclic(N)
     :: Generates a polynomial list of standard benchmark.

RETURN
     list

N
     integer

   * Function `katsura()' is defined in `katsura', and function
     `cyclic()' in  `cyclic'.

   * These functions generate a series of polynomial sets, respectively,
     which are often used for testing and bench marking: `katsura',
     `cyclic' and their homogenized versions.

   * Polynomial set `cyclic' is sometimes called by other name:
     `Arnborg', `Lazard', and `Davenport'.

     [74] load("katsura")$
     [79] load("cyclic")$
     [89] katsura(5);
     [u0+2*u4+2*u3+2*u2+2*u1+2*u5-1,2*u4*u0-u4+2*u1*u3+u2^2+2*u5*u1,
     2*u3*u0+2*u1*u4-u3+(2*u1+2*u5)*u2,2*u2*u0+2*u2*u4+(2*u1+2*u5)*u3-u2+u1^2,
     2*u1*u0+(2*u3+2*u5)*u4+2*u2*u3+2*u1*u2-u1,
     u0^2-u0+2*u4^2+2*u3^2+2*u2^2+2*u1^2+2*u5^2]
     [90] hkatsura(5);
     [-t+u0+2*u4+2*u3+2*u2+2*u1+2*u5,
     -u4*t+2*u4*u0+2*u1*u3+u2^2+2*u5*u1,-u3*t+2*u3*u0+2*u1*u4+(2*u1+2*u5)*u2,
     -u2*t+2*u2*u0+2*u2*u4+(2*u1+2*u5)*u3+u1^2,
     -u1*t+2*u1*u0+(2*u3+2*u5)*u4+2*u2*u3+2*u1*u2,
     -u0*t+u0^2+2*u4^2+2*u3^2+2*u2^2+2*u1^2+2*u5^2]
     [91] cyclic(6);
     [c5*c4*c3*c2*c1*c0-1,
     ((((c4+c5)*c3+c5*c4)*c2+c5*c4*c3)*c1+c5*c4*c3*c2)*c0+c5*c4*c3*c2*c1,
     (((c3+c5)*c2+c5*c4)*c1+c5*c4*c3)*c0+c4*c3*c2*c1+c5*c4*c3*c2,
     ((c2+c5)*c1+c5*c4)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3,
     (c1+c5)*c0+c2*c1+c3*c2+c4*c3+c5*c4,c0+c1+c2+c3+c4+c5]
     [92] hcyclic(6);
     [-c^6+c5*c4*c3*c2*c1*c0,
     ((((c4+c5)*c3+c5*c4)*c2+c5*c4*c3)*c1+c5*c4*c3*c2)*c0+c5*c4*c3*c2*c1,
     (((c3+c5)*c2+c5*c4)*c1+c5*c4*c3)*c0+c4*c3*c2*c1+c5*c4*c3*c2,
     ((c2+c5)*c1+c5*c4)*c0+c3*c2*c1+c4*c3*c2+c5*c4*c3,
     (c1+c5)*c0+c2*c1+c3*c2+c4*c3+c5*c4,c0+c1+c2+c3+c4+c5]

References
     *Note `dp_dtop': dp_dtop.

