@Carl Love 

Thank you.

How would I specify the differentiating variable if the function is of multiple variables?

@acer That's what I meant. Thank you.

@mmcdara Thank you but this is much more than what I need.

I just want functions that are not positive everywhere (in other words I want to discard expressions that are positive everywhere).

@Rouben Rostamian  Thank you. This is perfect. 

@sand15  Thank you so much!

@Carl Love 

This is very nice. I wish it were easier to do.

I have an additional question now. Would it be possible to animate this if there was another constant present (say for values of k from -1 to 1

(1+k)/(r^2*sin(theta)^2) 

@sand15 

sorry I should have made that clear r>0 and theta goes from -Pi to Pi. And want some sort of animation/plot that makes it easy to visualize where the function is greater than zero.

@Carl Love  I see this now, Thanks.

@mmcdara 

Hi thank you.

But I already know how to solve this pde manually. I wanted to practice my hand at doing this via maple.

I think having a benchmarking suite would be extremely helpful.

@C_R 

This is it. Thanks

@ecterrab I started with the differential geometry package and a lot of my scripts are written with the differential geometry package. I have been slowly moving towards the physics package.
Also exterior calculus seems to be a bit simpler in the differential geometry package. For example wedge products dont seem to have a simple equivalent in the physics package.

@acer I use the physics and differential geometry package. with physics package Petrov and Segre classification, calculation of the Riemann, Ricci and Einstein Tensor.
With Differential Geometry package Most of the time I calculate covariant derivatives, exterior derivatives.

With both packages a lot of my work involves using pdsolve to solve sets of equations and maple is very good at it.

Recently I have been wondering if getting better specs might significantly help with my work and hence my question.

@ecterrab  I think the post is asking why the Stress Energy tensor is nonzero for a vacuum solution.

@mmcdara  The only simplification tools I was aware of was simplify and subs.
I have gradly added this to my list.