# Thread: Simplying linear equation to get quartic in q with using Maple and using Descarte’s

1. ## Simplying linear equation to get quartic in q with using Maple and using Descarte’s

Using the maple I am trying to get quardic in q from this big linear equation. Then use Descarte’s rule of signs to determine the number of positive roots.

\frac{\gamma*q*P_Q}{k_p*(1-q)*P_C} = \frac{I*\alpha}{k_f+k_d+\frac{k_n*\lambda_b*\gamma *q*P_Q}{\lambda_b*\gamma*q*P_Q+k_p*\lambda_r*(1-q)^2}+k_p*(1-q)}

Values of parameters are given below:
$I=1200$
$k_f = 6.7*10.^7$
$k_d = 6.03*10.^8$
$k_n = 2.92*10.^9$
$k_p = 4.94*10.^9$
$\alpha = 1.14437*10.^(-3)$
$\lambda_b = 0.87e-2$
$\lambda_r = 835$
$\gamma = 2.74$
$P_C = 3*10.^(11)$
$P_Q = 2.87*10.^(10)$

=>
I tried the code in maple to get quartic in q but DOES NOT WORKS.

Code:
             II := 1200:
k_f := 6.7*10.^7:
k_d := 6.03*10.^8:
k_n := 2.92*10.^9:
k_p := 4.94*10.^9:
alpha := 1.14437*10.^(-3):
lambda_b := 0.87e-2:
lambda_r := 835:
ggamma := 2.74:
P_C := 3*10.^11:
P_Q := 2.87*10.^10:

eq := ggamma*q*P_Q/(k_p*(1-q)*P_C) = II*alpha/(k_f+k_d+k_n*lambda_b*ggamma*q*P_Q/(lambda_b*ggamma*q*P_Q+k_p*lambda_r*(1-q)^2)+k_p*(1-q)):

simply(eq, q);
My lecturer want me to manipulate the equation and get a quartic in q before substituting the values of parameters into the equation. After that,use Descarte’s rule of signs to determine the number of positive roots. Then write Q=1-q to get second quartic in Q and repeat rule of signs to determine number of steady states of q less than 1. And do the substition of parameters if necessary.
Now, its kind of hard for me what he wants because to get quartic in q first from the equation is hard to do by hand , so i have to use in maple which is not working then use Descarte’s rule of signs.

2. ## Re: Simplying linear equation to get quartic in q with using Maple and using Descarte

Posting a second time will not get you an answer any faster. Perhaps try different variable names.

Try using semicolons at the end of every statement instead of colons?

Also, try solve(eqn,q) instead of simplify(eqn,q)?

3. ## Re: Simplying linear equation to get quartic in q with using Maple and using Descarte

Originally Posted by SlipEternal
Posting a second time will not get you an answer any faster. Perhaps try different variable names.

Try using semicolons at the end of every statement instead of colons?

Also, try solve(eqn,q) instead of simplify(eqn,q)?
Maple understand the colons not semicolons sir. And i did tried the solve(eqn,q) to get the result for q which i got it. but this time i am trying to manipulate the equation to get quartic in q, so that i can use Descarte’s rule of signs to determine the number of positive roots. And after that do substitute parameters in and get the results for q.

4. ## Re: Simplying linear equation to get quartic in q with using Maple and using Descarte

Cross multiplying by hand should not be a problem.

\begin{align*}& \left[\left(k_f + k_d + k_p(1-q) \right)\left(\lambda_b\cdot \gamma \cdot q \cdot P_Q + k_p\cdot \lambda_r\cdot (1-q)^2\right) + k_n\cdot \lambda_b\cdot \gamma \cdot q \cdot P_Q \right]\left(\gamma \cdot q \cdot P_Q\right) \\ = & I\cdot \alpha\left( k_p(1-q)P_C \right)\left( \lambda_b\cdot \gamma \cdot q \cdot P_Q + k_p\cdot \lambda_r\cdot (1-q)^2 \right)\end{align*}

Ask maple to simplify that expression.