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9

Yes, this is a bug in the more general function RegionMeasure. I knew there were some edge cases in the handling of inexact numberics, but I was unaware of such a simple example. I will forward this bug internally. Workarounds include using the parametric (2-argument) form of ArcLength, and using DiscretizeRegion to preprocess regions before sending them ...


3

(1) Replace each variable by itself times a new variable (same new variable for all replacements). (2) Take nth derivative with respect to the new variable. (3) Set value of new variable to 1. I illustrate with n=2 and three variables. vars = {x, y, z}; D[(f @@ vars) /. Thread[vars -> t*vars], {t, 2}] /. t -> 1 (* z*(z*Derivative[0, 0, 2][f][x, y, ...


2

Try the following way. This: lst = Select[ Flatten[Table[{i, j, k, l}, {i, 0, 3}, {j, 0, 3}, {k, 0, 3}, {l, 0, 3}], 3], Abs[Total[#]] == 3 &] (* {{0, 0, 0, 3}, {0, 0, 1, 2}, {0, 0, 2, 1}, {0, 0, 3, 0}, {0, 1, 0, 2}, {0, 1, 1, 1}, {0, 1, 2, 0}, {0, 2, 0, 1}, {0, 2, 1, 0}, {0, 3, 0, 0}, {1, 0, 0, 2}, {1, 0, 1, 1}, {1, 0, 2, 0}, {1, 1, 0, ...


2

For example for f[___]= Sin[ x y z w] l = Flatten[ Permutations /@ (PadRight[#, 4] & /@ IntegerPartitions[3]), 1] (Derivative[##][f][x, y, z, w] & @@@ l) /. f -> (Sin[#1 #2 #3 #4] &)


1

In case you have expression like: expr =a Sin[x Exp[x]]; I would use: r = Integrate[expr,x]; If[FreeQ[r, Integrate, -1], Print["passed"], Print["failed"]]



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