@Doug Meade 

I agree with everything you said.  I am a complete amateur and was just trying to help someone in a MOOC.  There is definitely some conflict with the eigenvectors.  I don't know whether Maple is correct or Mathematica is correct.   I was able to get agreement between two of the three eigenvectors, at least to lowest order.  Interesting that such a relatively simple problem (eigenvectors of 3x3 matrix) should lead to these problems.

@acer 

What I find interesting is that the Heaviside function is undefined at zero (according to the Maple help pages), so normally I would think that using that function instead of the abs function might cause a problem.  But apparently the reverse is the case.

@acer 

There are probably lots of ways to get it to work, but I am curious why it failed in the first place, especially in the last couple of calculations where it works perfectly when I use a period of 2*Pi instead of a variable.  Also why would it get the integral correctly for cos and sin and fail for (cos + i*sin) - see line 3,4, and 6, which I would think would simply be evaluated as a linear combination.  I guess since it works if I keep the linear combination real, the problem lies in seeing complex numbers (which I thought was the Maple default) , and then maybe the program has a problem with the non-analytic absolute value function.  Anyway thanks for the help.

Mark

@Christian Wolinski 

In my opinion use of a standard provided LinearAlgebra package (I thought linalg has been deprecated), along with provided matrix entry palettes should give the same answer as use of matrix() entry commands.  If the provided palettes do not have the same functionality as command entries (and the matrices look identical), what use are they?  This is in my opinion a serious bug in the palettes and should be fixed.  As noted above this is not a bug in the LinearAlgebra package.

I was lead to believe that linalg package has been deprecated.  And if using the provided standard LinearAlgebra package along with provided Matrix entry palettes does not work then that is a bug in my opinion.and needs to be fixed.  The palettes should provide the same functionality as the actual entry commands (otherwise what is the use of them - especially since they lead to matrices that look identical to those from the matrix() entry command.

@acer 

Ok - it does work if I use the eval(map) construction, but this seems rather cluncky.  I am not a power user, just a theoretical physics wannabe, and from my perspective, these symbolic algebra programs seem to have a lot of bugs (though they are extremely powerful and useful), exactly where or in what package is not that relevant to me.  I am still waiting for a fix to my other major Maple complaint, that I and several others have had concerning the slowing down of the program and the constant greying out of palettes etc:

http://www.mapleprimes.com/questions/204422-Maple-2015-Constantly-Hesitates-To-Redraw

But I really appreciate the help,

Mark Weitzman

@acer 

Thank you very much, although this seems rather disturbing, as I use palettes all the time and never had a problem.  How do I set Normalizer?  As you can see I am a click and paste palette type of user (it is what attracted me to Maple over mathematica - shorter learning curve, and I couldn't pin the palettes in mathematica to the worksheet).  

Mark Weitzman

@markweitzman 

Could there perhaps be a problem entering the matrix using the matrix palette?  The following file that you posted and I downloaded executed fine.  But when I added a matrix via palette it again failed.

I think you are missing my point the code works but the display output on screen always involve dphi, dtheta etc instead of dφ etc. - it is much easier to read and understand complex metrics and curvature tensors if the actual greek symbols appear in the answers.

I think you are missing my point the code works but the display output on screen always involve dphi, dtheta etc instead of dφ etc. - it is much easier to read and understand complex metrics and curvature tensors if the actual greek symbols appear in the answers.