Hi,

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I suggest that Numeric3 offers the opportunity to drop the word rank from its lexicon. "rank" has an established usage long before digital computers. See: http://mathworld.wolfram.com/Rank.html

The meaning of "tensor rank" comes very close and was probably the inspiration for the use of this terminology in array system.

Yes: The total number of contravariant <http://mathworld.wolfram.com/ContravariantTensor.html> and covariant <http://mathworld.wolfram.com/CovariantTensor.html> indices of a tensor <http://mathworld.wolfram.com/Tensor.html>. The rank of a tensor <http://mathworld.wolfram.com/Tensor.html> is independent of the number of dimensions <http://mathworld.wolfram.com/Dimension.html> of the space <http://mathworld.wolfram.com/Space.html>.

I was thinking in terms of linear independence, as with Matrix Rank: The rank of a matrix <http://mathworld.wolfram.com/Matrix.html> or a linear map <http://mathworld.wolfram.com/LinearMap.html> is the dimension <http://mathworld.wolfram.com/Dimension.html> of the range <http://mathworld.wolfram.com/Range.html> of the matrix <http://mathworld.wolfram.com/Matrix.html> or the linear map <http://mathworld.wolfram.com/LinearMap.html>, corresponding to the number of linearly independent <http://mathworld.wolfram.com/LinearlyIndependent.html> rows or columns of the matrix, or to the number of nonzero singular values <http://mathworld.wolfram.com/SingularValue.html> of the map.

I guess there has been a tussle between the tensor users and the matrix users for some time.

If you come from the linear algebra, rank is the column or row space which is not the current usage in numarray but this is the Matlab usage. The matrix rank doesn't exist in numarray (as such, but can be computed) so the only problem for is remembering what rank provides and avoiding it in numarray.

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Perhaps some abbreviation for "Dimensions" would be acceptable.

The equivalent of "rank" is "number of dimensions", which is a bit long for my taste.

Perhaps nDim, numDim or dim would be acceptable.

There needs to be a clarification that by dimensions, one does not mean the number of rows and columns etc. However, taking directly from the numarray manual: "The rank of an array A is always equal to len(A.getshape())." So I would guess the best solution is to find out how people actually use the term 'rank' in Numerical Python applications. Regards Bruce