`sp', `sp_noalg'
----------------

sp(POLY)
sp_noalg(POLY)
     :: Finds the splitting field of polynomial POLY and splits.

RETURN
     list

POLY
     polynomial

   * Defined in the file `sp'.

   * Finds the splitting field of POLY, an uni-variate polynomial over
     with rational coefficients, and splits it into its linear factors
     over the field.

   * The result consists of a two element list: The first element is
     the list of all linear factors of POLY; the second element is a
     list which represents the successive extension of the field.  In
     the result of `sp_noalg' all the algebraic numbers are replaced by
     the special indeterminate associated with it, that is `t#i' for
     `#i'. By this operation the result of `sp_noalg' is a list
     containing only integral polynomials.

   * The splitting field is represented as a list of pairs of form
     `[root,' `algptorat(defpoly(root))]'.  In more detail, the list is
     interpreted as a representation of successive extension obtained
     by adjoining root's to the rational number field.  Adjoining is
     performed from the right root to the left.

   * `sp()' invokes `sp_norm()' internally. Computation of norm is done
     by several methods according to the situation but the algorithm
     selection is not always optimal and a simple resultant computation
     is often superior to the other methods.  By setting the global
     variable `USE_RES' to 1, the builtin function `res()' is always
     used.

     [101] L=sp(x^9-54);
     [[x+(-#2),-54*x+(#1^6*#2^4),54*x+(#1^6*#2^4+54*#2),
     54*x+(-#1^8*#2^2),-54*x+(#1^5*#2^5),54*x+(#1^5*#2^5+#1^8*#2^2),
     -54*x+(-#1^7*#2^3-54*#1),54*x+(-#1^7*#2^3),x+(-#1)],
     [[(#2),t#2^6+t#1^3*t#2^3+t#1^6],[(#1),t#1^9-54]]]
     [102] for(I=0,M=1;I<9;I++)M*=L[0][I];
     [111] M=simpalg(M);
     -1338925209984*x^9+72301961339136
     [112] ptozp(M);
     -x^9+54

Reference
     *Note `asq af af_noalg': asq af af_noalg, *Note `defpoly':
     defpoly, *Note `algptorat': algptorat, *Note `sp_norm': sp_norm.

