Platform: SGI
Package: Tensor
The help page for the function create() documents its first argument, index_char, as being an ordered list whose elements are either -1 or 1 indicating whether the corresponding tensor index is contravariant or covariant. A covariant index is described as denoted by a 1; a contravariant index by a -1.
The help page for the Riemann() command, also part of the tensor package, indicates that it returns the covariant components of the Riemann curvature tensor, which it claims are of character -1, which contradicts the documentation of the create() command. Also, in the example, the covariant components of the metric are described as being denoted by a -1, which contradicts the description of the command and also the documentation of the create() page.
The help page for the tensor package gives as an example the assignment of the covariant form of the Schwarschild metric using the create() command; it uses the notation that covariant indices are described by a -1 as well.
The help page for the Einstein() command refers to covariant indices on the metric as being denoted by 1 and covariant indices on the Ricci tensor as being denoted by -1; however, the example given on the same page denotes the covariant indices on the metric as being denoted by a -1.
The tensorsGR help page example uses [1,1] in the create() command for the covariant metric components; however, the output of the command claims that the character is [-1,-1] --- the opposite of the character given on input.
I’ve not gone through the other pages; I expect they are similarly confused.
What is the proper use of the tensor function? Is this a documentation problem, or is the tensor package unreliable?
I can’t help you with your specific questions, but you should consider looking at the GRTensorII package for Maple V (R3 and 4) which is available from Queen’s University in Canada. The WWW address is:
http://astro.queensu.ca/ grtensor/
My impression is that this package is more comprehensive and consistent than those built into Maple directly.