Checking the sign of an equation?

Questions
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1

Hello,

I have the following (simplified) problem:

f = fx fy - fz

fx>0

fy<0

fz>0

(with fx denoting f’(x), fy denoting f’(y) and fz denoting f’(z) )

How can I check, if f is positive or negative?

In this example it is obviously easy, in my calculation, it is definitely not, since it is very long and only consist of functions which are either greater or smaller than zero.

I am thankful for any help! And sorry, I’m a Mathematica beginner…

Tanks and best regards from Berlin!

2

Hi Fabian,

these are possibilities:

f := fx fy - fz;
Assuming[fx > 0 && fy < 0 && fz > 0, Simplify[f > 0]]

or

f := fx fy - fz;
Simplify[f > 0, Assumptions -> fx > 0 && fy < 0 && fz > 0]

Cheers,

Marco