1.2.9 `sm1.reduction'
---------------------

sm1.reduction([F,G,V,W]|proc=P)
     ::

RETURN
     List

F
     Polynomial

G, V, W
     List

P
     Number  (the process number of ox_sm1)

   * It reduces F by the set of polynomial G in the homogenized Weyl
     algebra; it applies the division algorithm to F. The set of
     variables is V and W is weight vectors to determine the order,
     which can be ommited.  `sm1.reduction_noH' is for the Weyl algebra.

   * The return value is of the form [r,c0,[c1,...,cm],[g1,...gm]]
     where G=[g1, ..., gm] and c0 f + c1 g1 + ... + cm gm = r.  r/c0 is
     the normal form.

   * The function reduction reduces reducible terms that appear in
     lower order terms.

   * The functions sm1.reduction_d(P,F,G) and sm1.reduction_noH_d(P,F,G)
     are for distributed polynomials.

     [259] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y]]);
     [x^2+y^2-4,1,[0,0],[y^4-4*y^2+1,x+y^3-4*y]]
     [260] sm1.reduction([x^2+y^2-4,[y^4-4*y^2+1,x+y^3-4*y],[x,y],[[x,1]]]);
     [0,1,[-y^2+4,-x+y^3-4*y],[y^4-4*y^2+1,x+y^3-4*y]]

Reference
     `sm1.start', `d_true_nf'

