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Question: Can I use Index notation in DifferentialGeometry?

Question:Can I use Index notation in DifferentialGeometry?

lsitongia 16 Maple
syntax differential-geometry
April 08 2010
0
I'm getting started with this. I'm reading books about General Relativity. Their notation uses superscripts and subscripts in Greek, for examples. But in the lessons for DifferentialGeometry and in applications I find in the Maple website, I see coordinate systems of (x,y), for example. Indices, raising and lowering, and other operations involve "d" and "D_" notation. Examples use something like T12 to represent what I would want to see as "T" with two subscripts having values of 1 and 2. I apologize if I'm not explaining the background to my question well. I'd simply like to know if it is possible to use superscripts and subscripts in tensors an have the analysis in Maple look just like it does in the textbooks. I would like to start with DGsetup([x_alpha],O]: where x_alpha would be represented in Maple as an "x" with a Greek alpha subscript, and have alpha go from 0 to 3, using Minkowski space, with the 0 index being the time part. Raising and lowering indices would do as expected, moving the Greek index up or down, instead of changing from "d" to "D_". Thanks, ==Leonard
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