# Re: Interesting Solution to a quartic eqn

*From*: Peter <pwolynes@xxxxxxxxx>*Date*: Sat, 13 Feb 2010 21:42:38 -0800 (PST)

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

.

**References**:**Re: Interesting Solution to a quartic eqn***From:*Arturo Magidin

**Re: Interesting Solution to a quartic eqn***From:*Peter

**Re: Interesting Solution to a quartic eqn***From:*Arturo Magidin

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