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Rewrite equilibrium variables in terms of another variable

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

anonymous user

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

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

dan_fulea gravatar imagedan_fulea ( 2017-09-18 04:32:20 +0200 )edit

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answered 2017-09-18 11:25:08 +0200

eric_g gravatar image

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(...).

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

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Last updated: Sep 18 '17