John Cremona on Sat, 25 May 2013 15:30:07 +0200 |
[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]
Re: Number of real roots of a polynomial |
For real cubics the number of real roots is either 1 or 3 depending on the sign of the discriminant, with some other cases easily distinguished if the discriminant is 0. That's not complicated, so I have no idea what you can have been asking Mathematica! John On 24 May 2013 20:59, Charles Greathouse <charles.greathouse@case.edu> wrote: > Thank you both, this is just what I needed. It's faster (30x) and more > accurate -- my old script failed (though in the conservative = "OK" > direction) a few times with large coefficients. > > Charles Greathouse > Analyst/Programmer > Case Western Reserve University > > > On Fri, May 24, 2013 at 3:51 PM, Bill Allombert > <Bill.Allombert@math.u-bordeaux1.fr> wrote: >> >> On Fri, May 24, 2013 at 03:41:49PM -0400, Charles Greathouse wrote: >> > Given a univariate polynomial, how can I determine the number of real >> > solutions with gp? >> > >> > Usually I look at polroots(P) and count the number of roots which have >> > an >> > imaginary part which 'looks like' 0. But I'd like a solution that >> > certifies >> > that the zeros are not merely close to being real. >> > >> > A solution giving the number of distinct real roots would be equally >> > useful >> > for me. Speed is important in this application, so if there's a good way >> > to >> > do it with the library that would be fine (though I'm just using GP >> > now). >> >> Assuming your polynomial is squarefree, polsturm will give you the answer. >> >> Try >> ???"real roots" >> >> Cheers, >> Bill. >> >