Richard Fateman schrieb:   
   >   
   > On 4/5/2016 9:47 AM, clicliclic@freenet.de wrote:   
   >   
   > > The scheme is not very hard to implement and quite useful to have   
   > > readily available. But perhaps one of the free Computer Algebra   
   > > systems offers something like this already?   
   > >   
   > quite useful? Maybe not compared to a good quality numerical   
   > polynomial root-finder.  Which I think all systems have, and are   
   > probably much faster even if not exact.   
   >   
   > This algorithm might have some relevance for   
   >   cylindrical algebraic decomposition, but CAD doesn't   
   > seem to require it.   
   >   
      
   Polynomial may be ill-conditioned such that numerical root finders have   
   severe difficulties locating some of the roots and placing error bounds   
   on them. As I recall, Mathematica therefore offers some such kind of   
   algebraic root bracketing in the complex plane as an alternative to its   
   error controlled numerics when it comes to keeping algebraic numbers   
   apart in symbolic computations.   
      
   Various complex root finders in the past have made use of this kind of   
   complex bracketing, at least as a fall-back strategy. For the algorithm   
   in the papers linked to, much of the symbolic computations can be done   
   for a parametrized polynomial - that is once for all for an entirely   
   symbolic disc to be checked for root inclusion. The algorithm might   
   therefore be attractive even as a stand-alone strategy for numerical   
   root finding in a computer algebra system.   
      
   Martin.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)