Re: Interesting Solution to a quartic eqn



Hi Professor Magidin:

Sorry about the error in my last post. I am pretty sure that for the
counter-example you produced (which is essentially when either a = 0
and |b|=1 or b=0 and |a|=1), you'll still have solutions, but you'll
lose the uniqueness part. Uniqueness will only hold when both a_0 and
b_0 ne zero and none of the a_j and b_j for j=1,...,n-2 which are
generated by this process, are zero also.

I hadn't considered the equations associated with (c2) to be
constraints, but now that you pointed this out, it makes sense.

Thank-you once again for the insights: I don't think I would have seen
most of them!

This problem is a small part of a much larger problem that deals with
fitting atmospheric tidal velocities to a model. Nevertheless, I'd
like to acknowledge your contribution to helping us better understand
the math behind this solution, with your permission of course.

Peter
.