How can I rewrite symbolic expression as a function of another symbolic expression?
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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
.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/542996/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543001/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543006/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543011/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543016/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543021/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543026/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543031/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543036/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543041/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543046/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543051/image.png)
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.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543056/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543061/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543066/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543071/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543076/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543081/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/543086/image.png)
Thanks for reading!
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