Tensor notation

[mikepowell]

For quite a long time I've been puzzled by the relationship between APL and tensor notation. I could see it was close but for the longest time I struggled with the details. I'd heard Ken Iverson speak about tensor notation as if it was nothing very special ... and this was Einstein's choice of notation.

So, I thought it was time to knuckle down and recast some classic tensor notation in APL. I'm working on a translation of general relativity and the theory of gravity into APL.

At this point I'm not quite ready to publish this. Rather, I'm looking for contacts, knowledgeable in both tensor notation and APL who could give me feedback. So, if you're interested, I'd appreciate your help.

TIA

Mike Powell
mdpowell@gmail.com

[JoHo]

Hi Mike,

It is a long time since I did some tensor calculus during my physics studies with APL.
What I found then, was that the two notations are quite different. I wasn't able to use
APL directly as a replacement notation, only when I had some numerical calculations to do,
APL was very useful.
In any case, I would be happy to try to help.

Kind Regards,
JoHo

[GDR]

Mike,
APL draws much inspiration from tensor notation - in particular multi-dimensional arrays and their operations. The big difference is that, in general, tensors involve arrays of functions rather than arrays of numbers.
You should look at the paper "The Derivative Operator" by Ken Iverson in the 1979 ACM conference proceedings for his heroic attempt to push APL further in this direction. Another paper you really must look at is "Physics in APL2" by Gregory Chaitin in which you will find APL2 functions to describe geodesics in curved space-time, and numerical verification of curvature near a black hole. You can download that fabulous paper from http://robertson.uk.net/chaitin.pdf .
Graeme.