I was asking some of my random matrix colleagues at Warwick a few days ago about a similar question, namely the probability that a "random" real polynomial of even degree had no real roots. (I was not even sure what the best probability distribution should be.) While not answering that precise question, I was given this reference http://arxiv.org/abs/1503.07926 which gives a closed formula for the prob. that a random 2n x 2n real matrix has no real eigenvalues. That might be useful (to the original questioner) even if it does not help his experiments.
John Cremona On 10 May 2015 at 19:11, Vincent Delecroix <[email protected]> wrote: > > > On 10/05/15 19:43, Dima Pasechnik wrote: >> >> >> On Sunday, 10 May 2015 18:22:42 UTC+1, Phoenix wrote: >>> >>> >>> Why can't you just take any arbitrary large degree polynomial and test? >>> >>> I am not getting you. >>> >>> I am on a very slow computer. >>> It will take me a long time to generate any example specifically relevant >>> to me. >>> That would involving running my rest of the code entirely. >>> >>> Isn't there a way for you to just randomly generate a 300 degree >>> polynomial? >>> >> >> 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 ;-) > > 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. -- 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.
