How can I rewrite symbolic expression as a function of another symbolic expression?

Suppose I want to evaluate an expression of the type with . Let and be functions of x and y, e.g. and . And I am able to show analytically that . Knowing that , I can now rewrite to the expression . With this I can now deduce that if .

However, I want to use a MATLAB script to approximate the exact value of the boundary of the circle/ellipse using a while loop that evaluates at a lower boundary a (where ) and b (where ), so that . However, I do not know how to make MATLAB rewrite my symbolic expression for as a function , so that I can substitute the boundaries a and b. I would be glad about suggestions on how to solve this type of problem.

Thanks for reading!

Answer 1

[Sai Veeramachaneni]

Hi,

You can leverage syms, diff functions to implement your functionality

Example:

syms x y
V = x^2+y^2

f1 = x
f2 = -x+y*(2-3*x^2-2*y^2)

g = f1*diff(V,x)+f2*diff(V,y)

Hope it helps