2.0. Important comments

1) Indices are the key objects in xTensor`, and the source of the generality of the system. They are carriers of contextual information, much like the decimal digits in numerical computations, or the letters in a text. An index by itself has little information (only an association to a vector space), but a group of indices together can encode a lot of information (rank, symmetries, metrics, bases, etc). In general, an index is anything which can be placed at an index-slot: that is, we shall later define four places in which we can put indices and anything which we can meaningfully put there will be called an index.

2) Starting version 0.9 of xTensor`, indices are associated to vbundles, and not to manifolds, as was the case in previous versions. This allows us to work with vbundles other than tangent bundles to manifolds.

3) We need a "language" to talk about indices, and though we usually understand what a dummy index or a covariant index is, such a language is not rigorously defined anywhere. I have invented my own language for this. Please, suggest changes if you find inconsistencies, gaps or bad choices.

4) Taken from the Internet:
    The plural of "index" for books, journals and newspapers is "indexes"; the plural of "index" for graphs and benchmarks for economics for example, is "indices"; but the plural of "appendix" is always "appendices".
I think the "index" of a tensor must follow the rule for the second group, and hence its plural will be "indices".

Created by Mathematica  (May 16, 2008)