`primedec_mod'
--------------

primedec_mod(PLIST,VLIST,ORD,MOD,STRATEGY)
     :: Computes decompositions of ideals over small finite fields.

RETURN
PLIST
     list of polynomials

VLIST
     list of variables

ORD
     number, list or matrix

MOD
     positive integer

STRATEGY
     integer

   * Function `primedec_mod()' is defined in `primdec_mod' and
     implements the prime decomposition algorithm in `[Yokoyama]'.

   * `primedec_mod()' is the function for prime ideal decomposition of
     the radical of a polynomial ideal over small finite field, and
     they return a list of prime ideals, which are associated primes of
     the input ideal.

   * `primedec_mod()' gives the decomposition over GF(MOD).  The
     generators of each resulting component consists of integral
     polynomials.

   * Each resulting component is a Groebner basis with respect to a
     term order specified by [VLIST,ORD].

   * If STRATEGY is non zero, then the early termination strategy is
     tried by computing the intersection of obtained components
     incrementally. In general, this strategy is useful when the krull
     dimension of the ideal is high, but it may add some overhead if
     the dimension is small.

   * If you want to see internal information during the computation,
     execute `dp_gr_print(2)' in advance.

     [0] load("primdec_mod")$
     [246] PP444=[x^8+x^2+t,y^8+y^2+t,z^8+z^2+t]$
     [247] primedec_mod(PP444,[x,y,z,t],0,2,1);
     [[y+z,x+z,z^8+z^2+t],[x+y,y^2+y+z^2+z+1,z^8+z^2+t],
     [y+z+1,x+z+1,z^8+z^2+t],[x+z,y^2+y+z^2+z+1,z^8+z^2+t],
     [y+z,x^2+x+z^2+z+1,z^8+z^2+t],[y+z+1,x^2+x+z^2+z+1,z^8+z^2+t],
     [x+z+1,y^2+y+z^2+z+1,z^8+z^2+t],[y+z+1,x+z,z^8+z^2+t],
     [x+y+1,y^2+y+z^2+z+1,z^8+z^2+t],[y+z,x+z+1,z^8+z^2+t]]
     [248]

References
     *Note `modfctr': modfctr, *Note `dp_gr_main dp_gr_mod_main
     dp_gr_f_main dp_weyl_gr_main dp_weyl_gr_mod_main
     dp_weyl_gr_f_main': dp_gr_main dp_gr_mod_main dp_gr_f_main
     dp_weyl_gr_main dp_weyl_gr_mod_main dp_weyl_gr_f_main, *Note
     `Setting term orderings': Setting term orderings, *Note
     `dp_gr_flags dp_gr_print': dp_gr_flags dp_gr_print.

