I am doing some rather complicated four-vector manipulations, which I would like to do with maple using the Physics package. My problem is this: I can't figure out how to define a specific four-vector. For example, one of my four-vectors is (p,0,0,p), while another is (p cos(theta), 0, p sin(theta), p). Here's my attempt:
**Checking the components using e.g. P1 shows this doesn't work.**
Then I tried defining the components myself, using:
P1:=p: P1:=0: P1:=0: P1:=p:
But when I try to have maple simplify P1_mu P1^mu, it just returns that expression (instead of zero). So, how to a define a specific spacetime four-vector, with the components I want (instead of an arbitrary one), and then how do I make Maple evaluate the products explicitly?
Thank you for your time!