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Topic: parameterizing a polynomial system
Replies: 9   Last Post: Dec 5, 2011 6:36 PM

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Dan Gelder

Posts: 15
Registered: 12/13/05
parameterizing a polynomial system
Posted: Dec 1, 2011 12:24 AM
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Hi r.math. I'm interested in taking a given system of polynomials, and
turning it into a parameterized system. For example, the ideal of
basic facts about a resistor:
< v - i*r = 0, i - v*g = 0, p - i*v = 0 >

I would like to turn it into the following system of functions given
any two variables. For example:

(r, g, v, i, p) in terms of r and v would be (r, 1/r, v, v/r, v^2 /
r )
(r, g, v, i, p) in terms of g and p would be (1/g, g, sqrt(p/g),
sqrt(p*g), p)

I can tell that there should be two parameters because there are five
variables and three equations, but another system could use a
different number.

Also I recognize that there are some sub-situations where one of the
variables is 0. For example if v is 0, that leaves only this possible
situation: (r, g, 0, 0, 0) since you can see that v, i, and p are all
simultaneous 0s and r and g are no longer linked to each other.

I have experience with Groebner bases and linear algebra, but was
wondering if anyone had a more solid (less guess-based) approach that
I could put into an algorithm. Thanks all.

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