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Question: Solving Three Equations?

Question:Solving Three Equations?

Andiguys 85 Maple , MaplePrimes
solve simultaneous-equations error
1 hour ago
0

How can we simultaneously solve three equations of the form:
w = f(Pn,Pr)
Pn = g(w,Pr)
Pr = h(Pn,w)

so that we obtain standalone expressions for w, Pn, and Pr?


 

> 

restart
> 

with(Optimization); with(plots); with(LinearAlgebra)
> 

_local(D)

D

 (1)
> 

``
> 

``
> 

D := 1-(Pn-Pr)/(1-delta)

1-(Pn-Pr)/(1-delta)

 (2)
> 

N := 2*delta*tau*(i2-tau+w)-2*tau*(i2-tau+w)+Cr*(i2-tau)*(Pn-Pr+delta-1); M := (4*delta-4)*tau+Cr*(Pn-Pr+delta-1)

2*delta*tau*(i2-tau+w)-2*tau*(i2-tau+w)+Cr*(i2-tau)*(Pn-Pr+delta-1)

  

(4*delta-4)*tau+Cr*(Pn-Pr+delta-1)

 (3)
> 

A := Cr*(M*(i2-tau)-N)/(tau*M^2); B := (delta-1)/M; lambda := alpha*D*(rho0*M/(1-delta)-Pr+w+Crm)

Cr*(((4*delta-4)*tau+Cr*(Pn-Pr+delta-1))*(i2-tau)-2*delta*tau*(i2-tau+w)+2*tau*(i2-tau+w)-Cr*(i2-tau)*(Pn-Pr+delta-1))/(tau*((4*delta-4)*tau+Cr*(Pn-Pr+delta-1))^2)

  

(delta-1)/((4*delta-4)*tau+Cr*(Pn-Pr+delta-1))

  

alpha*(1-(Pn-Pr)/(1-delta))*(rho0*((4*delta-4)*tau+Cr*(Pn-Pr+delta-1))/(1-delta)-Pr+w+Crm)

 (4)
> 

w := Pr-Crm-rho0*M/(1-delta)+lambda/(alpha*D); Pn := Cn+(1-delta)*(1-alpha*rho0-(Pr-w-Crm)*alpha*A+lambda*A)-(Pr-w-Crm)*alpha*rho0-Ce*rho0; Pr := Pn-(1-delta)*(1-alpha*rho0-(Pr-w-Crm)*alpha*A-lambda*A)-(Pr-w-Crm)*alpha*rho0-Ce*rho0

w

  

Error, recursive assignment

  

Error, recursive assignment

  
> 

``


 

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