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6

The following is not particularly fast and could be more accurate but does make progress toward the goals set in the Question. To begin, consider the analytical properties of f, as defined in the Question. By observation, it has branch points at {I Sqrt[6/5] ξ, I Sqrt[2/5] ξ} and their conjugates. Poles are obtained by p /. ...


4

Your cube file had a very large grid ( 117*117*130 = 1779570), and 2 million points is just far too many for testing a function. So I created cube files for the electron density and electrostatic potential for the molecule furan, using a much sparser grid (around 8000 grid points instead). Here they are: Density cube file Potential cube file Now that ...


4

Not an answer, but just a collection of results on my computer (Mac OS X 11.4) The timings are in seconds as reported by AbsoluteTiming. They are in the same order as the test cases provided by OP On Mathematica 8: {1.44, 1.33, 271.7, 0.000066} On Mathematica 9: {0.62, 0.61, 9.00, 0.00012} On Mathematica 10.3: {8.82, 8.78, 8.62, 0.00006} On ...


2

The answer is as you suspect - when you evaluate Dot[m1, m2, m3, m4, m5, ......m1000] the process is something like this: Look at the input: Dot[m1, m2, m3, m4, m5, ......m1000] Evaluate the first matrix product, m12=m1.m2 Look at the input: Dot[m12, m3, m4, m5, ......m1000] Evaluate the first matrix product, m123=m12.m3 Look at the input: Dot[m123, m4, ...



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