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I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that

Added note: This term has now been shown to vanish by a computer calculation, so that the action presented here does possess full local supersymmetry.

But the paper was written in 1976! Do you have any info what kind of computer and computer algebra system did they use? Is it documented anywhere?

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<a href=">Maxima</a>; existed then. You can still use it and download it. You could do numerical simulations of things using FORTRAN, too. – Jerry Schirmer Apr 20 '11 at 17:21
Jerry, you actually mean Macsyma rather than Maxima, right? ;-) – Luboš Motl Apr 20 '11 at 18:05
Also for the record schoonschip developed by Martinus Veltman existed – yayu Apr 20 '11 at 20:38
@Lubos, yes. I've never been good with the evolution of software from before my time. – Jerry Schirmer Apr 21 '11 at 13:25

Van Nieuwenhuizen's PhD advisor, Matinus Veltman, was arguably the first person to develop a computer algebra system in the early 1960s, and the program was used in the proof of renormalization of gauge theories.

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Does Schoonschip still exist? It would be nice to check it out. – Ron Maimon Feb 18 '12 at 17:56

It sounds like it may have been an early version of SHEEP, or some extension thereof. SHEEP was 'officially' released in 1977, but its predecessor, ALAM, was developed by d'Inverno in 1969. It was used to automate some of the complicated algebra in early calculations of the Bondi mass. You can read a bit about the history here: notes on SHEEP.

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(This is not really an answer, but here I have not yet enough reputation to post comments. If someone wants to move this to a comment, I won't object.)

1976 is not a particularly early date for computer calculations: Fermi, Pasta, and Ulam used computer simulations in the early 50s for their 1955 paper.

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But FPU is what computers are good at--- it is trivial to write this type of simulation of particles. Schoonship was doing algebraic manipulations, which is more difficult because it requires a parsing of a language. This only became automatic in the 70s, although, paradoxically, it is done less now than then because of the stultifying negative impact of the GUI on actual computation. – Ron Maimon Feb 18 '12 at 17:56

I don't know about this particular paper, but I do know that several early supergravity computations were checked using a computer algebra program 'Abra' written in Pascal by Mees de Roo. You could do gamma matrix algebra and Fierz transformations with it (among others), and it had a quite clever method to interactively work on parts of long expressions. This system was part of the inspiration for my own 'Cadabra' system.

I don't think Abra is publically available.

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