How Can I Determine Stability from Mathematica's Root Function Output?

[senan]

I'm kinda of messing around with a model of a biological system, I've found the equilibriums and decided I'd get the stability relations as well. I tried using mathematica to get the eigenvalues of the system to see if its stable or not and when I got the eigenvalues of my matrix mathematica kicked this back at me.


Root[a^2 *b^2*d*e^2 *m + 2 *a^3 *b *d*e *t *m + a^4 *d *t^2 *m + a*b^3 *g *d
*e *r+ a^2*b^2 *g*d*t*r + (a^2 *b^2d*e^2*m +a*b^2*e^3 *m + a^3 *b*d*e*t*m + 3a^2 *b*e^2*t*m +
2a^3 *e*t^2*m + a*b^3g*d*e*r) #1 + (b^3 *e^3*r +a*b^2 *e^2 *t*r) #1^2 + b^3*e^3*r #1^3 &, 1]

i know the # marks mean to input the function at address 1 in this case but seeing as i got the eigenvalues of a 3x3 matrix what would that be in this case

 

[CompuChip]

Basically it tries to tell you that the answer you are looking for is the solution of f(x) = 0 for some complicated f(x), but that it cannot solve that expression for x.

 

[Bill Simpson]

Sometimes, but not always it is possible to get the explicit form of a Root object in terms of radicals.

To do this wrap a ToRadicals[] around your Root object and in this example MMA can find it, but the result is more than triple the size. Simplify[] on that can reduce it down to something a little more than double the original size.

 

[senan]

Thanks for ye're replies. I think I'm going to have to go back and try and simplify th system a bit it. Hopefully I can reduce it down further by adjusting a few terms