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Apr
22
comment Are standard geometric functions present in Mathematica or do I have to type them in?
... as an example of the above comment you could evaluate {#, PolyhedronData[{"Pyramid", 4}, #]} & /@ {"Image", "VertexCoordinates", "SurfaceArea"} // TableForm.
Apr
22
comment Reduce gives wrong solutions
I wonder how this ties in with the documentation, which says "The result of Reduce[expr,vars] always describes exactly the same mathematical set as expr. ".
Apr
19
comment Efficient way to sum all the primes below $N$ million in Mathematica
FWIW, Total[Prime /@ Range[PrimePi[10^9]]] evaluates to 24739512092254535 — i.e. the same as your trial 2 result. The computation took a few minutes, and the peak kernel memory usage was about 4.7GB.
Apr
9
comment many indefinite integrals do not evaluate in 10.1, looking for the cause
I have seen cases with definite coefficients for which Mathematica gives the right or wrong answer depending on where the integration limits are located. As far as I could tell, the errors occurred when Mathematica was being inconsistent with how it handled different branches of the integrand.
Apr
9
comment many indefinite integrals do not evaluate in 10.1, looking for the cause
I suspect that this "regression" has to do with the presence of (complicated) branch points and branch cuts in the integrand, whose location depends on the value(s) of the parameter(s) in the integrand, and which have to be handled with extreme care if you want to get the correct result. Previously, Mathematica gave results that could be incorrect in such cases, so I presume Mathematica has been "regressed" whilst they work out a framework for handling such cases correctly.
Apr
6
comment Forcing solutions to avoid Root[]
The documentation says that ToRadicals[expr] attempts to express all Root objects in expr in terms of radicals.
Mar
30
revised General function for the expansion of a polynomial of operators
deleted 3 characters in body
Mar
30
revised General function for the expansion of a polynomial of operators
added 1 character in body
Mar
30
answered General function for the expansion of a polynomial of operators
Mar
16
revised Simplifying a product with indices by implementing a rule
added 317 characters in body
Mar
16
answered Simplifying a product with indices by implementing a rule
Mar
16
comment Quantum Physics question
In the matrix element that I quoted LegendreP[l, m, z] is the associated Legendre polynomial which gives the l dependence of the corresponding spherical harmonic.
Mar
16
comment Quantum Physics question
You don't need to integrate over \[Phi] because all your matrix elements are between states that have the same m. You can therefore evaluate Integrate[LegendreP[l1, m, Cos[\[Theta]]] Cos[\[Theta]] LegendreP[l2, m, Cos[\[Theta]]], {\[Theta], 0, \[Pi]}] for various l1, l2 and m to extract the results that you need.
Mar
13
comment How can I solve this expression?
To better visualise how to solve your problem, have a look at Plot[{Re[#], Im[#]} &[f[A]] // Evaluate, {A, -2, 2}], where f[A] is defined as the right hand side of your equation. Then you can use ContourPlot to extend the range of the plot to complex values of A.
Mar
9
comment Define action of noncommutative product of operators
Have a look at the answer that I gave to Non Commutative sorting in Mathematica, because it contains some tricks that might be sufficient to solve your problem.
Mar
5
comment Nonlinear matrix equation solving in Mathematica
C is a "reserved word" in Mathematica, so don't use it — preferably, begin every user-defined symbol name with a lowercase character. You could NMinimise (w.r.t. the components of x) an objective function defined as #.#&[a.x+b.Exp[x]-c] — i.e. the norm-squared of the difference between the left and right hand sides of your equation.
Mar
4
comment Calculate the matrix M such M.X=omega
Is this the sort of thing you want to do? Array[M, {3, 3}].X == \[Omega] // Thread // SolveAlways[#, {\[Theta]'[t], \[Phi]'[t], \[Psi]'[t]}] &
Feb
26
comment Correcting image distortion by warping a set of distorted points to a corresponding set of undistorted points
FindGeometricTransform might do what you want.
Feb
22
comment How do I plot lat/long points in the Atlantic Ocean?
Did you mean to use GeoPosition /@ data rather than Reverse /@ data?
Feb
17
comment What are the limits to file size for Import[ file.wav,“WAV”]
You can find what elements there are in a WAV file by evaluating Import[<file name>, "Elements"], where <file name> includes the .wav extension. I just tried this on a WAV file and got {"AudioChannels", "AudioEncoding", "Data", "SampledSoundList", "SampleRate", "Sound"}.