`gr_minipoly', `minipoly'
-------------------------

gr_minipoly(PLIST,VLIST,ORDER,POLY,V,HOMO)
     :: Computation of the minimal polynomial of a polynomial modulo an
     ideal

minipoly(PLIST,VLIST,ORDER,POLY,V)
     :: Computation of the minimal polynomial of a polynomial modulo an
     ideal

RETURN
     polynomial

PLIST  VLIST
     list

ORDER
     number, list or matrix

POLY
     polynomial

V
     indeterminate

HOMO
     flag

   * `gr_minipoly()' begins by computing a Groebner basis.
     `minipoly()' regards an input as a Groebner basis with respect to
     the variable order VLIST and the order type ORDER.

   * Let K be a field. If an ideal I in K[X] is zero-dimensional, then,
     for a polynomial P in K[X], the kernel of a homomorphism from K[V]
     to K[X]/I which maps f(V) to f(P) mod I is generated by a
     polynomial. The generator is called the minimal polynomial of P
     modulo I.

   * `gr_minipoly()' and `minipoly()' computes the minimal polynomial
     of a polynomial P and returns it as a polynomial of V.

   * The minimal polynomial can be computed as an element of a Groebner
     basis.  But if we are only interested in the minimal polynomial,
     `minipoly()' and `gr_minipoly()' can compute it more efficiently
     than methods using Groebner basis computation.

   * It is recommended to use a degree reverse lex order as a term order
     for `gr_minipoly()'.

     [117] G=tolex(G0,V,0,V)$
     43.818sec + gc : 11.202sec
     [118] GSL=tolex_gsl(G0,V,0,V)$
     17.123sec + gc : 2.590sec
     [119] MP=minipoly(G0,V,0,u0,z)$
     4.370sec + gc : 780msec

References
     *Note `lex_hensel lex_tl tolex tolex_d tolex_tl': lex_hensel
     lex_tl tolex tolex_d tolex_tl.

