How can I define f(x) = x/x in MATLAB (Symbolic Computation)

I try with these commands

x = sym('x');
f(x) = sym('f(x)');
f(x) = x/x;

and

f(x) = sym('x/x');

, and both of them produce

f(x) = 1

(yes.. for every real x included 0)

The question is how I can avoid the pre-evaluation in the command "sym", or there exists another way to handle this problem.

Thank you very much!

Answer 1

[Star Strider]

I’m obviously missing something in your post. Wouldn’t (x/x)=1 for all x under any conditons?

[epsilonxe]

x/x is not equal to 1 when x is only zero.

Please consider the following

if f(x) = x/x then Domain of f is R-{0}.

if f(x) = 1 then Domain of f is R.

[Star Strider]

If x=0 then the function is undefined (or NaN in the IEEE standard), but you are defining the function here as a symbolic. The symbolic engine automatically simplifies it.

If you want it to behave in a mathematically correct way, create it as an ‘anonymous function’ instead. (These are allowed in the Symbolic Math Toolbox as well as the rest of MATLAB.) I did it here by hand, but you can use matlabFunction to do it for you.

For example:

syms x
f = @(x) x/x
y = f(0)

produces:

y =

               NaN

as you want it to.

[epsilonxe]

Thank you very much for your answers. This is what I want.

I missed the point that x/x is symbolically 1. Thanks again for this prompt.

Moreover I still have one more question:

Is there a method to avoid automatic simplification on "sym/syms" commands?

(just want to store the value "as is" via sym/syms)

[Star Strider]

My pleasure!

The various MATLAB Toolboxes still teach me about them. The occasional version differences keep it interesting.

I’m not aware of a way to automatically suppress it, since simplifying expressions is likely the reason most people use the various symbolic engines. I believe that it (and others like Maple and Mathematica) automatically simplifies to an extent.

I experimented just now with the assume command, and got a very interesting result:

syms f(x)
assume(x == 0)
f(x) = x/x
g = symfun(x/x, x)

In this experiment, f and g both evaluate to 1, even with x ‘set’ to zero. I suggest you report this as a bug.

Answer 2

[Sean de Wolski]

MuPad can handle a function like x/x without automatic simplification. I'm not sure why you want this though. Why do you care about it, is it just for display or something else?

[epsilonxe]

x/x is not equal to 1 when x is only zero.

Please consider the following:

Let f(x) = x/x and g(x) = 1 then domains of f and g are R - {0} and R respectively.

The automatic simplification in "sym/syms" may leads to lose some info.