Force symbolic variable to be constant

I would like to know if there is a way to impose that a symbolic variable is constant with respect to differentiation, for example.

I have a symbolic variable (e.g. z) which depends on other symbolic variables (e.g. x and y), and it is part of an expression that I want to differentiate. However, I want to impose that z is effectively a constant, so even if it depends on x and y it should not be differenciated with respect to these variables.

I can not substitute x and y by their numerical values, so I need an alternative way to set z as a symbolic constant.

syms x,y,z

z = x + y;

(then I would apply the desired method)

diff(z,x) (and ideally this would be zero)

Thank you in advance

Answer 1

[Rahul]

Hi Jose,

As of MATLAB R2024a, there is no direct functionality for treating a dependent variable or symbol as constant while performing an operation w.r.t. the associated dependent variables, like differentiation. However, a workaround for such a scenario could be initializing another symbol, which could then be treated as a constant in the expression, depending on the use case:

% Define symbolic variables 
syms x y z z_d 

% Define relations between variables 
z = x + y; 

% Define an example expression taking constant or independent variable z_d 
expr = z_d*x*y; 

% Differentiate express w.r.t. required symbol 
const_expr = diff(expr, x) 

While declaring an expression, z_d and z can be used depending on whether z has to be treated as a constant or variable respectively and later subs function could be used to interchange the symbols for the other case.

% Substitute dependent variable z instead of independent symbol z_d 
var_expr = subs(const_expr, z_d, z) 

% Perform some operation 
...

% Simplify resulting expression to required number of steps
simple_expr = simplify(var_expr, 'Steps', 2) 

This will allow you to interchangeably use constant or variable z in an expression and perform subsequent operations.

For further information regarding defining symbols and expressions or differentiation, you can refer to the Symbolic Math Toolbox documentations:

https://www.mathworks.com/help/symbolic/symbolic-variables-expressions-and-functions.html

https://www.mathworks.com/help/symbolic/differentiation.html

Hope this helps!