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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