Can we distinguish between variables and parameters in a symbolic function?

Hello,

I have a simple (perhaps naive, if so my appology) question. Consider the following

syms x f(x) x

f(x) = a*x;

Is there a way to distinguish between 'x' and 'a'? If I use symvar(f) it just gives the information about all vars and aparetly

cannot distinguish between x and a.

Any idea?

Thanks in advance,

Babak

[Dyuman Joshi]

symvar determines symbolic variables in the expression. Since you have not defined a as a symbolic variable in the above code, symvar won't classify a as an output.

What is the data type of a?

[Mohammad Shojaei Arani]

Sorry, that was just a typo, which I correct now

syms x f(x) a

f(x) = a*x;

Answer 1

[Dyuman Joshi]

syms f(x) a m n z
f(x)=a*x

f(x) = 

y=symvar(f)

y = 

I understand what you mean by 'cannot distinguish between x and a'

But, this is how syms variable are expressed in arrays. For example -

z=[m n]

z = 

x and a are expressed similarly in the above expression obtained from symvar

However, you can convert the symbolic expression to string and obtain seperate variables -

z=symvar(char(f))

z = 2×1 cell array
    {'a'}
    {'x'}

[Mohammad Shojaei Arani]

Thanks Dyuman!

Well, still there is no way to distinguish between 'x' and 'a'.

If MATLAB does not have such a capability then I believe MathWorks should include this. In high level mathematical analysis as well as high level pogramming this is needed (My opinion. They decide about it).

[Dyuman Joshi]

How exactly do you want to distinguish between x and a?

[Mohammad Shojaei Arani]

for instance, it could be through a logical variable using a function I call 'isparameter' as bellow

symvar(f)

[x, a]

isparameter(symvar(f))

[0, 1]

[Torsten]

@Mohammad Shojaei Arani

What in your opinion is a remarkable difference between a variable and a parameter in symbolic computations that would justify to distinguish between the two ? I don't see any.

If you want to distinguish between them, I suggest you give them adequate names, e.g. var_a or para_a.

[Dyuman Joshi]

What is the logic behind this?

[Mohammad Shojaei Arani]

Hi Torsten and Dyuman,

After I thought deeper I came to believe that you are right. Thanks for your time.

Math is somehow different than programming :-)

Answer 2

[Walter Roberson]

https://www.mathworks.com/help/symbolic/sym.argnames.html

f_variables = argnames(f)
f_param = setdiff(symvar(f), f_variables)

This is not the same thing as "all variables mentioned that are not parameters". symvar does not report any "bound" variables or any variables being used as functions.

A bound variable is like x in

int(f(x), x, a, b)

provided that f does not itself contain x then you could substitute any other variable name without affecting the output, like

int(f(Dummy), Dummy, a, b)

int() and symsum() and symprod() can all use bound variables.

[Mohammad Shojaei Arani]

Hi Torsten,

So, it is actually possible to do it in matlab. Nice!

You also answered another question of me (somehow you read my mind!).

Thanks a lot for the very useful helps!

Babak