I'm wondering how to replace the equilibrium variables in terms of another one. I want the equilibrium to be in terms of a new varible called R = beta*o/(u+y)(u+o) and I can't seem to find the right function that would allow me to do this.
Equilibrium point: S= (u+y)(u+o)/beta*o Want: S = 1/R
Here is a possible solution:
sage: var('beta o u y R')
(beta, o, u, y, R)
sage: S = (u+y)*(u+o)/(beta*o)
sage: S.subs(solve(R == beta*o/((u+y)*(u+o)), beta)).simplify_full()
1/R
Explanations: you have first to introduce R as a symbolic variable; this is what is done in the first line above. Then you express one of the other symbolic variables in terms of R; here we choose beta:
sage: solve(R == beta*o/((u+y)*(u+o)), beta)
[beta == (R*o*u + R*u^2 + (R*o + R*u)*y)/o]
This outcome is then used to perform the substitution in S via the function S.subs(...).
Asked: 2017-09-18 00:05:33 +0100
Seen: 164 times
Last updated: Sep 18 '17
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Please define variables and make clear, what is given. Then relation to be checked. Also, please give a clear formula for $R$, if $R$ is given. Is it, as you write it: $$ R =\beta\cdot \frac o{u+y}\cdot (u+o)\ ?$$