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  • $\begingroup$ If you have a function roots that gets the roots of a polynomial into a list form of consistent dimension, then why not something like: Select[polys, Not[0!=Norm[roots[#]]!=1] &] $\endgroup$ Commented Aug 6, 2020 at 18:08
  • $\begingroup$ I assume that by $S^1$ you mean that unit circle in the complex plane? So you are allowing complex roots? Just for clarification. $\endgroup$ Commented Aug 6, 2020 at 20:34
  • $\begingroup$ Apparently there is something called the Jury stability criterion which you can use to determine if the roots of a polynomial are all inside the unit disk. $\endgroup$ Commented Aug 6, 2020 at 20:42
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    $\begingroup$ Are "roots of undesirable magnitude" related to "rodents of unusual size"? $\endgroup$ Commented Aug 8, 2020 at 16:33
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    $\begingroup$ R.O.U.M.s? I do not think they exist. $\endgroup$ Commented Aug 11, 2020 at 2:58