How to check if a symbolic function is positive or negative?

Hi everyone,

I've defined a square function this way:

sym x

y = x^2

Running the command ' isAlways(y>=0) ' I get:

Warning: Unable to prove '0 <= x^2'.

> In symengine

In sym/isAlways (line 42)

Why Matlab is displaying the warning?

Thanks in advance for who will help me!

Answer 1

[Steven Lord]

MATLAB is unable to prove that y is always greater than or equal to 0 because y is not always greater than or equal to 0. Here is a case where it is:

x = 1;
y = x^2

y = 1

y >= 0 % true

ans = logical
   1

Here is a case where it is not.

x = 1i;
y = x^2

y = -1

y >= 0 % false

ans = logical
   0

If you told MATLAB that x was real, it would help.

syms x real
y = x^2

y = 

isAlways(y >= 0)

ans = logical
   1

[Andrea Strappato]

Thank you Steven!