Simplify symbolic expressions with custom constraints

Is it possible to algebraically simplify a symbolic expression based on a custom assumption on the symbolic variables?

Let's take a simple example. Suppose we have:

syms x y
u = x^3 + x * y^2 + y ;

Let's say we want to add the following assumption on the symbolic variables:

x^2 + y^2 = 1

Upon which, u would simplify to

u = x + y

Is something like this possible?

I stumbled upon the following related pages, but none seemed to enable adding a custom expression for the simplification

https://de.mathworks.com/help/symbolic/simplify-symbolic-expressions.html

https://de.mathworks.com/help/symbolic/simplify.html

https://de.mathworks.com/help/symbolic/choose-function-to-rearrange-expression.html

[Weixin Wang]

Would be really helpful if someone has a method!!

Answer 1

[Walter Roberson]

No it is not possible.