prove that symbolic equation is always greater than 0 in matlab

To prove that a symbolic equation is always greater than 0 in Matlab, you can use the assume function to set specific assumptions for the variables in the equation. Then, you can use the isAlways function to check if the equation is always greater than 0 under those assumptions.

Here's an example code snippet:

main.m
syms x y z
assume(x > 0)
assume(y < 1)
assume(z, 'real')
eqn = x*y + z > 0;
isAlways(eqn)
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In this example, we have defined three symbolic variables x, y, and z, and set some assumptions for them using the assume function. Then we have defined an equation eqn that combines these variables, and added the condition that the equation should always be greater than 0. Finally, we use the isAlways function to check if this condition holds true for all possible values of x, y, and z under the given assumptions.

If the output of isAlways is true, then the symbolic equation is always greater than 0 under the given assumptions. Otherwise, you may need to adjust the assumptions or the equation itself to prove the inequality.