I am wondering about this one actually:

On Wednesday, May 30, 2012 6:24:33 AM UTC-7, Dima Pasechnik wrote:
>
> Or "finiding a parametric representation of the solutions"? 


This is (one of )   a (large number) of problems I have been wondering 
about for awhile.
And maybe finding a representative, but I haven't decided yet that I want 
to peek at answers to that one, so say I just wanted to know about making a 
parametric representation.

I am happy to grant in advance arbitrary constraints which illustrate the 
approach.  For example, lacking any real idea how to handle quadratic 
inequalities, I will do things like clamp them to *equality* and work out 
the system that way, then go back through and... uh... undo the latches on 
the inequalities one at a time.

But.  um.  So far I have only done that when I can reliably linearize, 
which isn't really answering the question.

This strikes me as a heck of a tricky problem.

Oh.  is it a lie and write, say,  x{i}x{j} as X{ij}, and pretend to 
linearize that way?  Does this go anywhere?  Again, I failed to find a 
general parameterization which was more than an aesthetic change.  Unless, 
of course, I had enough terms that the pairwise system could be directly 
solved, and then linearized.

I apologize if these questions are naive.  I'm having a hard time getting 
the shape of this problem into my head.


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