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Dec
18
comment $\tt SphericalHarmonicY$ does not seem to be an eigenfunction of the spherical harmonic equation
Another data point: if you use FunctionExpand[FullSimplify[(* stuff *)]] on the full eigenvalue PDE, you get True as the result. So, it can simplify that, but it cannot do the intermediate step of simplifying your expression to a single instance of SphericalHarmonicY[].
Dec
18
revised Evaluating an integral
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Dec
18
revised Can't inject EncryptedObject
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Dec
18
comment How to solve an equation system whose equations are based on Mod[x,y]
Nevertheless, that this can even be contemplated is a reason why LCGs are worse than useless in cryptographic applications.
Dec
18
comment more numerically accurate inverse matrix
"I have to multiply this inverse matrix with other matrix" - then yes, you are solving a linear system. As to why LinearSolve[] is acting like this for a manifestly Hermitian system, I don't yet have any ideas.
Dec
18
comment How to solve an equation system whose equations are based on Mod[x,y]
That's why it's a comment and not an answer. Anyway, have you seen this?
Dec
18
comment more numerically accurate inverse matrix
"I am not solving linear system" - in other words, you are not multiplying this inverse matrix with anything else, are you?
Dec
18
revised $\tt SphericalHarmonicY$ does not seem to be an eigenfunction of the spherical harmonic equation
deleted 5 characters in body
Dec
18
comment How to solve an equation system whose equations are based on Mod[x,y]
This generates your example numbers pretty quickly: BlockRandom[SeedRandom[12345678, Method -> {"Congruential", "Multiplier" -> 314159269, Increment -> 453806245, Modulus -> 2^31}]; RandomReal[1, 4, WorkingPrecision -> 20]]
Dec
18
comment $\tt SphericalHarmonicY$ does not seem to be an eigenfunction of the spherical harmonic equation
Even if one uses FullSimplify[], the problem seems to be in the fact that Mathematica does not seem to recognize a particular difference equation satisfied by the associated Legendre polynomial.
Dec
18
revised hippocrates moons for any shape
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Dec
18
comment How to use BSplineFunction for calculating derivative
Why not use Interpolation[] instead?
Dec
18
revised Limits explanation in doc
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Dec
18
comment Looking for an extensive gallery of Mathematica's 2D graphics
Have you seen this?
Dec
18
comment Help with calculating a complicated integral
"the singularities of Hypergeometric1F1" - the Kummer function is holomorphic (no poles or branch cuts), so your bet is way off in this case.
Dec
18
comment Help with calculating a complicated integral
"The correct answer" - how are you getting the correct answers? Why not use that method instead?
Dec
17
comment Piecewise Function, Explanation of Extra Case
"every possible value of $x$" - I don't see your construction covering complex arguments; recall that Mathematica assumes everything is complex unless told otherwise.
Dec
17
revised more numerically accurate inverse matrix
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Dec
17
comment more numerically accurate inverse matrix
You know SetPrecision[], right?
Dec
17
comment more numerically accurate inverse matrix
What happens if you try the computations at higher precision? In any case, LinearSolve[] is still preferable over Inverse[].