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Aug
6
comment Why does GridLines option fail with Function?
Yes, this is a work-around. I would just include Legended as an allowed Head for the plot argument, because otherwise it won't work with the PlotLegends options.
Aug
5
comment How get eigenvectors without phase jump?
@xslittlegrass I added more details about the Bloch sphere that I mentioned earlier. In that method, I implement the same constraint as I originally stated, but without having to divide by a potentially small number.
Aug
5
comment How get eigenvectors without phase jump?
@xslittlegrass Sure, that's one of the infinitely many alternative conditions one could require. What I did was just a choice I thought appropriate for the particular problem at hand. For eigenvectors in two-dimensional complex vector spaces one also often uses the Poincaré (or Bloch) sphere.
Aug
4
comment How to make Eigensystem in version 10 produce the same results as version 9
@acl Right - your answer to the other question (which got closed) could perhaps be combined with mine to give a canonical answer. If xslittlegrass rephrases the question to be more general maybe it could remain open to serve that purpose... (sorry I have to leave right now...)
Aug
3
comment Finding unit tangent, normal, and binormal vectors for a given r(t)
@murray But on the other hand, once you understand the procedure, I think you'd want a convenient way to access it - and therefore having it available in canned form is good, instead of making your own library.
Aug
2
comment Higher derivative
Please use correct Mathematica syntax and be more specific as to the form of the result you expect. Also look at Quick Hessian matrix and gradient calculation - this may be a duplicate.
Aug
2
comment Substituting values in 3j symbols
Although this is true, I don't think that it explains the incorrect behavior.
Aug
2
comment Substituting values in 3j symbols
The same incorrect result also happens when I replace ThreeJSymbol with ClebschGoradan in the first line.
Jul
29
comment Integrating Mathematica in Blackboard
I think currently Blackboard doesn't allow you to access external URLS for JavaScript and CSS from within HTML files that you upload. This means you will have to try and download all the remote files needed by the CDF plugin embed script, and put them into a directory together with the CDF file and the HTML file that contains the embed code. Then you could try to zip that whole directory and upload it to Blackboards under "Files > upload ZIP file...". I haven't actually tried it because I don't really have much use for CDF files anyway...
Jul
27
comment Can NDSolve handle discountinuos data?
I think this is a regression: your code produces the expected answer with no problem in Mathematica version 8.
Jul
26
comment How can I mend this broken heart?
(+1) To make it work in version 8, I defined CubeRoot[x_] := (Abs[x]^(1/3) Sign[x]).
Jul
25
comment Result of Integrate depends on order of integration although the domain is rectangular
@MichaelE2 I agree, and I think version 10 should recognize the divergence more quickly, as is the case in version 8 (and apparently in 9). Maybe it gets stuck in trying to combine some ConditionalExpressions. Don't have time to investigate right now...
Jul
25
comment Result of Integrate depends on order of integration although the domain is rectangular
The fact that integration order matters in this case seems to be due to the fact that the integration in r goes to infinity, so the domain isn't compact. However, I do agree that the behavior of Mathematica has changed, and it would be good to understand better why that is.
Jul
24
comment Mathematica 10 fails to calculate integral that Mathematica 9 can handle
@MitchellKaplan Here is a nice tool you can install in order to format your code with Greek letters etc.: Additional useful buttons for our M.SE editor
Jul
23
comment Symbolic solution(s) to generalized Heat equation
Do your comments always run this long? Just kidding. In the Heat function, you should add Assumptions->t>0 to the Integrate to speed it up and avoid ConditionalExpression in the output.
Jul
23
comment Symbolic solution(s) to generalized Heat equation
I would rather not try to broaden the question so much. It's basically a task for a curator to gather the existing Green's functions for various problems. Fully automating this would require a lot of effort: recognizing the type of equation, bringing it to some standard form etc. This would not fit into the format of a Q&A site like this, I think.
Jul
22
comment Symbolic solution(s) to generalized Heat equation
@chris Yes, that's true, it's a trick that works for the heat equation and also the Schrödinger equation. I omitted a bunch of steps that would be needed to get there from the spectral integral as one usually finds it in textbooks. The general relation for the Green's function in terms of eigenfunctions is however also something that could be automated. Only enforcing the convergence of the integral may in general be a problem. That's where specific tricks come in handy. What I showed is the shortest possible calculation I know of, for this case (i.e., the heat eq. in the question).
Jul
22
comment Symbolic solution(s) to generalized Heat equation
Not sure either, but I up-voted yours to cancel the downvote. Anyway, as your answer shows there is potential for generalizations. But I did say that already, too... so really this isn't a separate answer to the original question. It's more a comment.
Jul
22
comment Symbolic solution(s) to generalized Heat equation
@chris Upping the dimensions is one possibility, and automating the Green's function is another. Both can be automated to some extent - which is to say that there is definitely room for Wolfram to add some functionality. But yes, it should be possible for us to do some of their work for them... with the caveat that it will probably break in less standard cases (e.g., elliptical coordinates are already much harder).
Jul
22
comment HoldForm doesn't hold form
Great analysis and solution for the main issue - it also works for FrameLabel where the same issue appeared.