# Revision history [back]

### simple numerical solve

Hello, I'm trying to solve a fairly simple 1 variable equation, but the output I get is:

[g_a == -31375155/31496372sqrt(-4/5g_a + 1) + 31375155/31496372sqrt(4/5g_a + 8) - 35/8]

Is there a simple way to get a closed-form solution? Hopefully without installing a numerical optimization routine? I have not been able to get simplify to work for this.

Thank you!!

### simple numerical solve

Hello, Hello,

Thanks for the help, I'm trying to move from Mathematica to Sage, but I'm still having some trouble with the basics. Specifically, I'm moving from 1-var to 2-var numerical optimization/solver. I want to optimize function g or, equivalently, solve a fairly simple 1 variable equation, but the output the system of first-order conditions, f. So far, I have not been able to get is:

[g_a == -31375155/31496372sqrt(-4/5g_a + 1) + 31375155/31496372sqrt(4/5g_a + 8) - 35/8]

any of the scipy routines to work. Is there a simple way to get a closed-form solution? Hopefully without installing a numerical optimization routine? I have not been able to get simplify to work for this.

Thank you!!do this?

Thanks! jv

# Constants

y_a = 50 y_b = 50 x = 40 alpha_a = .2 alpha_b = .2

# Functions

v(n)= n^.5 v1(n) = derivative(v(n),n) u(n)= n^.5 u1(n) = derivative(u(n),n)

# Variables

var('g_a') var('x_a')

# Optimization

g = (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f1 = ((1-alpha_b)v1(g_a+alpha_b(x - g_a)))/((1-alpha_a)v1(x-g_a+alpha_a(g_a)))==(v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f2 = (u1(x_a)/u1(x-x_a)) == (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f(g_a, x_a) = (f1, f2)

### simple numerical solve

Hello,

Thanks for the help, I'm trying to move from Mathematica to Sage, but I'm still having some trouble with the basics. Specifically, I'm moving from 1-var to 2-var numerical optimization/solver. I want to optimize function g or, equivalently, solve the system of first-order conditions, f. So far, I have not been able to get any of the scipy routines to work. Is there a simple way to do this?this? (Note: the objective function is concave wrt to both arguments.)

Thanks! jv

# Constants

y_a = 50 y_b = 50 x = 40 alpha_a = .2 alpha_b = .2

# Functions

v(n)= n^.5 v1(n) = derivative(v(n),n) u(n)= n^.5 u1(n) = derivative(u(n),n)

# Variables

var('g_a') var('x_a')

# OptimizationOptimization (over [0, x])

g = (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f1 = ((1-alpha_b)v1(g_a+alpha_b(x - g_a)))/((1-alpha_a)v1(x-g_a+alpha_a(g_a)))==(v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f2 = (u1(x_a)/u1(x-x_a)) == (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f(g_a, x_a) = (f1, f2)

### simple numerical solvesolve (2-variables!!)

Hello,

Thanks for the help, I'm trying to move from Mathematica to Sage, but I'm still having some trouble with the basics. Specifically, I'm moving from 1-var to 2-var numerical optimization/solver. I want to optimize function g or, equivalently, solve the system of first-order conditions, f. So far, I have not been able to get any of the scipy routines to work. Is there a simple way to do this? (Note: the objective function is concave wrt to both arguments.)

Thanks! jv

# Constants

y_a = 50 y_b = 50 x = 40 alpha_a = .2 alpha_b = .2

# Functions

v(n)= n^.5 v1(n) = derivative(v(n),n) u(n)= n^.5 u1(n) = derivative(u(n),n)

# Variables

var('g_a') var('x_a')

# Optimization (over [0, x])

g = (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))(v(x-g_a+alpha_a*(g_a))-u(y_b)+u(y_b-(x-x_a)))

f1 = ((1-alpha_b)v1(g_a+alpha_b(x - g_a)))/((1-alpha_a)v1(x-g_a+alpha_a(g_a)))==(v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f2 = (u1(x_a)/u1(x-x_a)) == (v(g_a+alpha_b(x-g_a))-u(y_a)+u(y_a-x_a))/(v(x-g_a+alpha_a(g_a))-u(y_b)+u(y_b-(x-x_a)))

f(g_a, x_a) = (f1, f2)