Re: Problems with high-dimensional lists

*To*: mathgroup at smc.vnet.net*Subject*: [mg2532] Re: [mg2494] Problems with high-dimensional lists*From*: Allan Hayes <hay at haystack.demon.co.uk>*Date*: Thu, 16 Nov 1995 01:46:49 -0500

Begin forwarded message: Sascha Unzicker<Sascha at sunmail.lrz-muenchen.de,Unzicker at lrz.uni-muenchen.de> Problems with high-dimensional lists Reports the following a=Table[0,{3},{4},{5},{6}]; Dimensions[a] {3, 4, 5, 6}, a[[1,1]]=Table[x,{6},{5}]; (*1*) Dimensions[a] {3, 4} Transpose[a,{4,1,2,3}]; Transpose::tperm: Permutation {4, 1, 2, 3} is longer than the dimensions {3, 4} of the array. Sascha: After (*1*), a is no longer a cuboidal array. Dimensions only goes as deep as the cuboidal structure. This is also shown by TensorRank[original a] being 4 and TensorRank[a after (*1*)] being 2. A simpler example of the effect is a=Table[0,{2},{1}] {{0}, {0}} TensorRank[a] 2 Dimensions[a] {2, 1} a[[1]] = {1,2} {1, 2} a {{1, 2}, {0}} TensorRank[a] 1 Dimensions[a] {2} Transpose[a] Transpose::nmtx: The first two levels of the one dimensional list {{1, 2}, {0}}cannot be transposed. Transpose[{{1, 2}, {0}}] Allan Hayes hay at haystack.demon.co.uk