( --> Dick Henry's web page )

      ... has discovered (and is causing to be corrected) a serious deficiency in Mathematica!

Here's how it happened! Way back in 1995, I wrote my program to create Mathematica scripts for General Relativity.

( One result was an Astrophysical Journal paper, Kretschmann Scalar for a Kerr-Newman Black Hole )

Inspired by this, I continued to evalute all 17 Zachary & Macintosh (zm) scalars, with no difficulty, using Mathematica 2.2.2

( Well, I say "with no difficulty," but the fact is, that to calculate all 17 for a Kerr-Newman Black Hole, even today,
takes longer than 24 hours on a Macintosh G5 desktop! )

Then came the shock! Mathematica 3.0 came out (in 1996), and it proved to be incapable of evaluating zm16, or zm17, at all!

I emailed Steve Wolfram, and he referred the matter to an assistant, but nothing came of it at that time. [Finally fixed (2008) ... in Mathemtica 7.0 ! ]

So, I forgot about it. Hey, what the heck!

But! With the announcement that Macintosh is moving to Intel chips, there will no longer be a Classic mode!

And Mathematica 2.2.2 is Mac-Classic!

I would lose my ability to re-calculate these fascinating scalar invariants! Tragedy loomed!

So! Once again I emailed Steve Wolfram, and this time I persisted, and Mathematica responded nobly!

And, a few days ago, Mathematic provided a temporary patch, which I call "mathematicaPatch," which allows successful calculation of zm16 !


Check it out for yourself! First, take a look at the 2.2.2 result:

Good-Result using Mathematica 2.2.2

Probably you can't repeat that, because you don't have 2.2.2 (Hey, I may be the only person in the world with a copy!)

But, you can sure as heck check out that mathematicaPatch works (and also, that Mathematica 5.2 is helpless without it):

simply copy the file below into your Mathematica, and hit "enter."

Bad-Result using Mathematica 5.2

Well, that is the happy ending!

However, mathematicaPatch is not a panacea. I tried using it in my "all up" program, and it only works in certain cases.

I am hoping, and expecting, that when Mathematica 6 comes out, a complete fix will be incorporated.

updated 2006 February 1     by our Webmaster


(Above is the cleaned-up version, with the multiple-angles that Mathematica insists on removed by brute force.)