Becoming friends with my ex?

So after breaking up with my ex (whom I currently work with.) Things went south for awhile and we stopped talking all together. She is however, someone I dont really want to lose as a friend, so I have been trying to remedy the situation.

So far we are back to being able to talk to each other and mutually work with one another. Some days are even very pleasant and I can laugh and smile with her. a lot of days though, there are many times when I will try to spark a conversation or simply say hi and I'm given a cold shoulder. Times when if she overhears a conversation between me and coworkers she will chime in and sometimes poke fun at me or belittle me. Sometimes even give me a light punch or something.

I know she isn't interested anymore at least, I'm pretty sure she is with someone. But the back and forth hot and cold I get from her makes me unable to tell sometimes if she really wants to be friends or if I'm just a nuisance she has to live with because we work together. She tells me she cares a lot about me and that's why she picks on me so much, so I just take it at face value but I dont know.

What is your take? Is it something that should just get better with time? Or should i just give up trying to rekindle a friendship.
Becoming friends with my ex?
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