def dup_expand(polys, K):
 if (not polys):
  return [K.one]
 f = polys[0]
 for g in polys[1:]:
  f = dup_mul(f, g, K)
 return f

def dup_expand ( polys , K ) : if ( not polys ) : return [ K . one ] f = polys [ 0 ] for g in polys [ 1 : ] : f = dup_mul ( f , g , K ) return f
multiply together several polynomials in k[x] .