Ask Your Question

# Rewrite equilibrium variables in terms of another variable Anonymous

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

edit retag close merge delete

## Comments

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: $$R =\beta\cdot \frac o{u+y}\cdot (u+o)\ ?$$

## 1 Answer

Sort by » oldest newest most voted

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(...).

more

## Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

## Stats

Asked: 2017-09-18 00:05:33 +0200

Seen: 70 times

Last updated: Sep 18 '17