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 Jun23 comment Excel column label from integer To clarify: if, say, the function is named spreadsheetColumn[], then spreadsheetColumn[27] should return "AA"? Jun23 comment How to choose three points on the circle so that the triangle is not a right triangle? Maybe include Circle[{-2, -1}, 5] too, to facilitate visualization. Jun23 comment Solving this system of equations produces an error message about badly conditioned matrix You'll want to look at Eigensystem[]. Jun23 comment Measuring the area of non analytical regions in a plot I don't see you mentioning your "different reasons"; if you have the points comprising your curves, you can at the very least use the "shoelace formula" or fancier methods to get a good estimate of the area. Jun23 comment Numerical Integration with InverseErfc This is an answer, but apparently not for this question. Jun22 comment Trace of FullSimplify "if it is possible for Mathematica to show the steps" - not in this case, I believe. Jun22 comment Trace of FullSimplify In general, the simplification methods internally used by Mathematica do not necessarily correspond to how one might simplify by hand; remember that a method that is simple for computers to do is not necessarily simple for humans, and vice-versa. Jun22 comment How to maximize a function over a rotation matrix? I don't have Mathematica on me at the moment, but you might try {Array[K, {3, 3}], {p, q, r}, a, b} /. Last[NMinimize[Flatten[{Total[MapThread[SquaredEuclideanDistance, {f[#, Array[K, {3, 3}], {p, q, r}, a, b] & /@ x, y}]], Thread /@ Thread[Transpose[Array[K, {3, 3}]].Array[K, {3, 3}] == IdentityMatrix[3]], Det[Array[K, {3, 3}]] == 1, a > 0, b > 0}], Flatten[{Array[K, {3, 3}], {p, q, r}, a, b}]]]... Jun22 comment How to maximize a function over a rotation matrix? ...and some example points would be, y'know, cool too... Jun22 comment How to maximize a function over a rotation matrix? Some more definiteness would be appreciated; in particular, what would your $f$ typically look like? Jun22 comment Change of coordinates for an InterpolatingFunction I'm not sure; after all, this is undocumented functionality... Jun22 comment How to maximize a function over a rotation matrix? In that case, you really should edit your question to talk about your actual problem, and maybe include sample data and expected results... Jun22 comment How to maximize a function over a rotation matrix? You will want to look up FindGeometricTransform[]; it will be able to find the best rigid transformation between your two sets of points. Jun22 comment Have the Random functions changed? No problem; I couldn't contribute much otherwise since I'm not using a machine with Mathematica at the moment... Jun22 comment Have the Random functions changed? Actually, digging deeper into old docs, it would seem that the legacy method in fact uses the rule 30 cellular automaton in the integer case. This is borne out by the fact that "Legacy" and "Rule30CA" give identical results for RandomInteger[]. In short, version 8 uses "ExtendedCA" as the default, while version 9 uses "Rule30CA" by default, for both random integers and reals. Now we wait for somebody from WRI to explain this switch... Jun22 comment Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer I'm not quite sure why one works and the other doesn't, even though they are ostensibly equivalent; the reason I left a comment is because I am not at a machine with Mathematica. Might I suggest writing your own answer to your own question instead? Jun22 comment Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer Did you already try Assuming[Element[n, Integers], 2/Pi Integrate[Cosh[a x] Cos[n x], {x, 0, Pi}]]? Jun22 comment Have the Random functions changed? Well, for completeness' sake, could you also do tests replacing RandomInteger[{-9, 9}, 10] with RandomReal[1, 10]? Maybe use InputForm[] so that all the digits of the random variates are displayed... BTW, to cover the default method in the results of the Table[], you can use the setting Method -> Automatic. Jun22 comment Have the Random functions changed? Huh, that's a step back. Here I thought they replaced the legacy generator with the newer CA-based ones precisely because the legacy method had not too good statistical properties... Jun22 comment Have the Random functions changed? To give a particular example, what does BlockRandom[SeedRandom[42, Method -> "ExtendedCA"]; RandomInteger[{-9, 9}, 10]] return on version 9?