Here is an example of a real-rooted polynomial generated by my code: 1296*x^24 - 20736*x^22 + 129600*x^20 - 393984*x^18 + 584496*x^16 - 362880*x^14 + 62208*x^12
This I know to be real-rooted because I tested this in Mathematica. In general my code will generate polynomials of degree ~200-300 Then is there a way to test real-rootedness inside SAGE itseld? And given some other number (typically as a squareroot of some other integer) can I test if the largest root is below that threshold? On Sunday, May 10, 2015 at 3:09:48 PM UTC-5, vdelecroix wrote: > > On 10/05/15 21:51, Dima Pasechnik wrote: > > On Sunday, 10 May 2015 19:11:27 UTC+1, vdelecroix wrote: > >> On 10/05/15 19:43, Dima Pasechnik wrote: > >>> A random polynomial for sure won't have the properties your polynomial > >>> probably has (e.g. all roots real). > >> > >> Nope, but the characteristic polynomial of a "random" matrix in SL(d,R) > >> would ;-) > >> > > > > really? I'd say a random symmetric matrix in M_d(R), yes, surely, but > not > > in SL_d(R)... > > Depends on your definition of random. If you pick any non-degenerate > generating set and look at a random product of length > d^2 then yes. > > Though, I do not know for the definition of random as "uniform on all > matrices in SL_d(R) with coefficients less than N". > > Vincent > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
