Solving a system of equations.

For

and

where

How do I write a code that will take a given x and y value and output an alpha and delta value?

[jgg]

Do you want a numerical solution or a symbolic solution?

Answer 1

[Vineeth Kartha]

Hi Christopher,

The following lines of code will do the trick:

>> syms alpha delta
>> solver = @(x,y) solve(x ==alpha / delta^2 , y ==(( (3*alpha*(1+delta)^2) + ( (1+alpha)*(1+alpha*delta^2)))^(0.5))/((1+alpha)^2), alpha, delta,'IgnoreProperties', true);
>> sol = solver(x,y);

Pass the desired values of x and y to the function named "solver". This will return a structure that contains the values of "alpha" and "delta", for the given x and y values.

Refer to the MATLAB documentation of solve for more details.

[Christopher Marlar]

This is what I get as an output when I try to run the solver.

Warning: Possibly spurious solutions.

In symengine
In mupadengine/evalin (line 102)
In mupadengine/feval (line 158)
In solve (line 292)
In Alpha_Delta>@(x,y)solve(x==alpha/delta^2,y==(((3*alpha*(1+delta)^2)+((1+alpha)*(1+alpha*delta^2)))^(0.5))/((1+alpha)^2),alpha,delta,'IgnoreProperties',true)

[Walter Roberson]

Your delta is always squared so algebraically both negative and positive values are valid. The message is warning you that multiple solutions have been returned but that they might not all make sense in the overall context.