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## tensor.diderot: demo of some details of how tensors work In Diderot, vectors (rank-1 tensors), matrices (rank-2 tensors), and tensors generally are objects with some number of ordered indices. This program demonstrates indexing and contraction, with either `•` or `:`. The printed results can be used to determine how these depend on index ordering. Assuming the directions at https://github.com/Diderot-Language/examples this program can be compiled with: ../../vis12/bin/diderotc --exec tensor.diderot Like Mathematica, Diderot doesn't enforce a semantic distinction between row and column vectors, but the following assumptions should not create any surprises. In a rank-2 tensor, i.e. a matrix, the first index is into the rows, and the second index is into the columns. A matrix is created by `mm = [[a,b,c],[d,e,f],[g,h,i]]` would conventionally be written as: a b c d e f g h i This program also demonstrates how differentiation increases tensor rank with the help of a small 3-vector dataset `vec.nrrd`, created with the help of a [program in a later example, `fs3d-vec`](../fs3d): ../fs3d/fs3d-vec -width 10 -angle 30 -axis 1 2 3 -which 2 -sz0 30 -sz1 25 -sz2 20 | unu save -f nrrd -o vec.nrrd rm -f out.nrrd The vector-valued function sampled by this field over (x,y,z) should be: [1.4*x, 2*y + 0.2*x + 0.4*x*x, 4*z + 0.1*x + y*z] This function has an intentionally non-symmetric Jacobian, and some isolated elements in the second derivative, for the testing purposes here. Note that things commented out and tagged with `RSN` refer to capabilitites that should be working hopefully real soon now.

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