On Monday, 11 May 2015 06:43:22 UTC+1, Phoenix wrote: > > > 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. > > well:
sage: p=1296*x^24 - 20736*x^22 + 129600*x^20 - 393984*x^18 + 584496*x^16 - 362880*x^14 + 62208*x^12 sage: p.roots() [(-2, 2), (2, 2), (-sqrt(sqrt(3) + 2), 1), (sqrt(sqrt(3) + 2), 1), (-sqrt(-sqrt(3) + 2), 1), (sqrt(-sqrt(3) + 2), 1), (-sqrt(3), 1), (sqrt(3), 1), (-1, 1), (1, 1), (0, 12)] if all the monomials have even degree you certainly should replace x^2 by y... > 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.
