FW: roots of quartic equation (fwd)

[Matthias Winkler <Matthias dot Winkler at cern dot ch>]

Dear GSL developers!

May I forward you this question about the root of quartic polynomial 
equations in GSL. Will there be a dedicated gsl_poly_solve_quartic 
function?

Cheers,
Matthias 

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---------- Forwarded message ----------

-----Original Message-----


Hi Antonis,

I have already replaced the two CERNlib calls in the global and local 
algorithms with GSL equivalents. In the RICH we have one remaining, 
which is drteq4 (roots of quartic equation 
http://consult.cern.ch/shortwrups/c208/top.html) in the RichDetTools 
packages. I think this call might be slightly tricky to change to GSL 
since I couldn't find a direct replacement in GSL. The nearest I could 
get was (http://sources.redhat.com/gsl/ref/gsl-ref_6.html#SEC52) 
gsl_poly_complex_solve which solves general n-degree polynominals. The 
funny thing is that, as GSL themselves quote in the manual "The roots of

polynomial equations cannot be found analytically beyond the special 
cases of the quadratic, cubic and quartic equation" but as far as I can 
tell they only provide analytic functions for quadratic and cubic 
equations.

May be we should try the general equation ? - but I am slightly worried 
that since it uses an iterative approach it may not work as well as the 
CERNLIB call. Another (less tidy) possible solution would be to 
transplant the CERNLIB routines into the package, and effectively use a 
private version of the CERNLIB call. What do you think ?

cheers  Chris