How can I set higher-order to1

For example, I have a function

f1=x^3*y^2*z+x^2*z+x^2*y*z^3;

let x^n=x,y^n=y,z^n=z,

so my function becomes

f1=x*y*z+x*z+x*y*z

=2x*y*z+x*z

Is there a built-in command to realize it?

Answer 1

[Jyothis Gireesh]

There may not be an in-built function to replace all the higher order terms in a polynomial with their corresponding single order terms.

But, you may use the following workaround which makes use of symbolic substitution function “subs()” to achieve the same result.

clear; 
syms x y z f1(x,y,z); 
f1(x,y,z) = x^3*y^2*z + x^2*z + x^2*y*z^3; 
n = 3; 
f2 = subs(f1(x,y,z),[x.^(2:n) y.^(2:n) z.^(2:n)],[repelem(x,n-1) repelem(y,n-1) repelem(z,n-1)]); 

Here “n” is the highest power of all the variables in the polynomial.

Please refer to the following documentation which explains about simultaneously performing multiple substitutions in a symbolic function.

https://www.mathworks.com/help/symbolic/subs.html#btqh8bz-1

Hope this helps!!