Isaac Mancero Mosquera

Attacking a mathematically silly idea is not attacking you. Stop the drama.

Sure. If that coefficient is not 1, you can't apply this method and the code is not useful. What's so wrong with that? Are you aware that Not all theorems apply when you want, but when their logic premises hold true?

If the purpose of this file was the mapping of general polynomial forms, then you'd be right and this would be a different story.

You are not reading my answer well: The depressed form can be used in a NON-EQUATION context, meaning not in a problem of the form: p(x)=0. In THAT case, it's better for the user to normalize whatever thing they want by themselves.

Please note:

Roots of p(x)=0 are unchanged by multiplication by a scalar.

Roots are changed in the case of p(x)=K. If you normalize p(x), then you should normalize K. Since K is nowhere to be found in my file, that task should be left to the user.
[Because delferro.m has a more general mapping of a polynomial unrelated to root-findings methods, so you shouldn't go around happily multiplying polynomials!].

You may like to multiply coefficients just because you want. But you are not supposed to do so in whatever context.

IF (big IF) your problem is related to findings roots, then it would be ok, but then again, there is already a built-in Matlab function to do that.

IF (again big IF) you are dealing with the functional w=p(x), you can normalize BOTH sides in your equation, or apply a more general solution, which is not exactly "divide by the coefficient of x^3", but applying another change of variable to obtain the monic trinomial form.

I hope it's clear now why this function will not divide by the coefficient of x^3 (the general mapping formulation won't do it either).

"Thank you for the feedback. I will improve this script with a better help section and possibly a change in the name" but I'm repeating myself here.

I don't feel attacked if you criticize my program, I'm actually thankful, since programming is not my cup of tea. Also, I always welcome critics; working in Science, I have to be prepared to debunk and be debunked, there is nothing personal in it; but if we disagree in something, we have to proceed separate ways -still nothing personal in it.

I'm uploading a new version of the file soon.

Attacking a mathematically silly idea is not attacking you. Stop the drama.

I'll try to be more clear, for the sake of Math (I agree with all your observations regarding the programming). This two polynomials:

p(x) and q(x)=K*p(x) are different.

They even have the same roots:

p(x)=0 and q(x)=0 at the same "x".

But they are not the same as functionals, and this is best seen when wee equal them to "w" non zero:

p(x)=w & q(x)=w have not the same solutions.

Multiplying polynomials by constants is a very popular method when finding roots, or when you have the other side of the equation p(x)=w, then:

K*p(x) = K*w , still mathematically correct.

In my program, there is no a hint of any equation, is just a mapping of a polynomial from one form to other.

That's why I put a warning to the user, they might want to multiply and normalize, but they do that themselves, at their own risk; because this program does not have "w" (from p(x)=w) as an input.