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### numerical computation of roots (maple equivalent of fsolve) of a system of nonlinear equations with multiple variables parameters

Hi All, the following is my code:

# Parameters:

k0 = 0.1 kd = 0.05 k1 = 20 j1 = 0.1 km1 = 0.2 jm1 = 0.1 k2 = 0.055 j2 = 0.1 pPTEN = 0.001 dPTEN = 0.0054 k3 = 0.006 j3 = 2 k4 = 0.15 j4 = 0.1 km4 = 73 jm4 = 0.5 pMdm2 = 0.018 dMdm2 = 0.015 dMdm2s = 0.015 k5 = 0.024 j5 = 1 k6 = 10 j6 = 0.3 km6 = 0.2 jm6 = 0.1 n1 = 3 n2 = 3 PIPtot = 1 AKTtot = 1

# Variables to solve

p53 = var('p53') AKTs = var('AKTs') Mdm2 = var('Mdm2') Mdm2s = var('Mdm2s') PIP3 = var('PIP3') PTEN = var('PTEN')

AKT = AKTtot - AKTs PIP2 = PIPtot - PIP3

# Rate Equations

v0 = k0 v1 = (k1 * PIP3 * AKT) / (j1 + AKT)
vm1 = (km1 * AKTs) / (jm1 + AKTs)
v2 = (k2 * Mdm2s * p53) / (j2 + p53)
v3 = (k3 * ((p53)^n1))/(((j3)^n1) + ((p53)^n1)) v4 = (k4 * PIP2)/(j4 + PIP2) vm4 = (km4 * PTEN * PIP3)/(jm4 + PIP3) v5 = (k5 * ((p53)^n2))/(((j5)^n2) + ((p53)^n2)) v6 = (k6 * Mdm2 * AKTs)/(j6 + Mdm2) vm6 = (km6 * Mdm2s)/(jm6 + Mdm2s)

ss_p53 = v0 - v2 - kdp53 ss_AKTs = v1 - vm1 ss_PIP3 = v4 - vm4 ss_PTEN = pPTEN + v3 - dPTEN * PTEN ss_Mdm2s = v6 - vm6 - dMdm2sMdm2s ss_Mdm2 = pMdm2 + v5 - v6 + vm6 - dMdm2*Mdm2

# Equation to Solve

z = solve([ss_p53==0, ss_AKTs==0, ss_PIP3==0, ss_PTEN==0, ss_Mdm2s==0, ss_Mdm2==0],\ [p53, AKTs, PIP3,PTEN, Mdm2s, Mdm2])

End Code

I tried using Sage "solve" to analytically solve the system of equations. I got a "FloatingPointError: Floating point exception"

I thought of ways to get round this exception by 1) using log and exp in my math equations -- I can't work round this 2) I have no idea how to create exceptions for this since I can't access the sub-solutions while the solutions are still underway 3)Then I tried maxima.solve --> no roots could be found

Maybe, this problem can't be solved analytically, so I thought maybe I could do so numerically. Hence my following question,

I can only find functions that tackle univariate equations. Is there a sage equivalent of maple's f-solve which numerically computes all roots of multivariate system of nonlinear equations without the need of initial conditions?

Thanks a lot! I would really appreciate this

Rgds Samantha

 2 No.2 Revision calc314 4151 ●21 ●48 ●111

### numerical computation of roots (maple equivalent of fsolve) of a system of nonlinear equations with multiple variables parameters

Hi All, the following is my code:

### ### Begin Code

 Parameters: Code##### #Parameters: k0 = 0.1 kd = 0.05 k1 = 20 j1 = 0.1 km1 = 0.2 jm1 = 0.1 k2 = 0.055 j2 = 0.1 pPTEN = 0.001 dPTEN = 0.0054 k3 = 0.006 j3 = 2 k4 = 0.15 j4 = 0.1 km4 = 73 jm4 = 0.5 pMdm2 = 0.018 dMdm2 = 0.015 dMdm2s = 0.015 k5 = 0.024 j5 = 1 k6 = 10 j6 = 0.3 km6 = 0.2 jm6 = 0.1 n1 = 3 n2 = 3 PIPtot = 1 AKTtot = 1 Variables 1 #Variables to solve solve p53 = var('p53') AKTs = var('AKTs') Mdm2 = var('Mdm2') Mdm2s = var('Mdm2s') PIP3 = var('PIP3') PTEN = var('PTEN') var('PTEN') AKT = AKTtot - AKTs PIP2 = PIPtot - PIP3 Rate Equations PIP3 #Rate Equations v0 = k0 v1 = (k1 * PIP3 * AKT) / (j1 + AKT) vm1 = (km1 * AKTs) / (jm1 + AKTs) v2 = (k2 * Mdm2s * p53) / (j2 + p53) v3 = (k3 * ((p53)^n1))/(((j3)^n1) + ((p53)^n1)) v4 = (k4 * PIP2)/(j4 + PIP2) vm4 = (km4 * PTEN * PIP3)/(jm4 + PIP3) v5 = (k5 * ((p53)^n2))/(((j5)^n2) + ((p53)^n2)) v6 = (k6 * Mdm2 * AKTs)/(j6 + Mdm2) vm6 = (km6 * Mdm2s)/(jm6 + Mdm2s) Mdm2s) ss_p53 = v0 - v2 - kdp53 kd*p53 ss_AKTs = v1 - vm1 ss_PIP3 = v4 - vm4 ss_PTEN = pPTEN + v3 - dPTEN * PTEN ss_Mdm2s = v6 - vm6 - dMdm2sMdm2s dMdm2s*Mdm2s ss_Mdm2 = pMdm2 + v5 - v6 + vm6 - dMdm2*Mdm2 Equation dMdm2*Mdm2 #Equation to Solve Solve z = solve([ss_p53==0, ss_AKTs==0, ss_PIP3==0, ss_PTEN==0, ss_Mdm2s==0, ss_Mdm2==0],\ [p53, AKTs, PIP3,PTEN, Mdm2s, Mdm2]) Mdm2]) End Code
Code 

I tried using Sage "solve" to analytically solve the system of equations. I got a "FloatingPointError: Floating point exception"

I thought of ways to get round this exception by 1) using log and exp in my math equations -- I can't work round this 2) I have no idea how to create exceptions for this since I can't access the sub-solutions while the solutions are still underway 3)Then I tried maxima.solve --> no roots could be found

Maybe, this problem can't be solved analytically, so I thought maybe I could do so numerically. Hence my following question,

I can only find functions that tackle univariate equations. Is there a sage equivalent of maple's f-solve which numerically computes all roots of multivariate system of nonlinear equations without the need of initial conditions?

Thanks a lot! I would really appreciate this

Rgds Samantha