Another sad loss, with the death of Joachim Neubüser this week.
He was the driving force behind the creation of the computer algebra system GAP. Even though I worked with John Cannon, the creator of the rival system Magma, I have always used GAP rather than Magma. That for several reasons:
- Magma is expensive, GAP is free, and I am mean. Neubüser is supposed to have said, “Nobody charges you for using Sylow’s Theorem, so nobody should charge you to compute a Sylow subgroup.”
- It had unlimited precision integer and rational arithmetic, which was absolutely necessary for some of the computatations I did – indeed, before I started using GAP, I had written my own unlimited precision integer routines in Pascal. Along with everything else, I use GAP as a calculator.
- It happened that I have always had GAP expertise close at hand: Leonard Soicher at QMUL, Olexandr Konovalov and a number of others at St Andrews. Indeed, Leonard wrote the GRAPE package for computing with graphs and groups, which I have made huge use of.
Related to the second point, back in 2008 I spent six months in Cambridge running a programme at the Isaac Newton Institute. Jan Saxl very kindly arranged for me to be a visiting fellow at Gonville and Caius College, which gave me the use of a flat in Rose Crescent. At the time Rosemary was recovering from cancer treatment, so it was possible to come to Cambridge and spend her time in the flat apart from short walks. She had just been on an RSS panel investigating the distastrous failure of a drug trial at Northwick Park, and had invented some better designs for first-in-human drug trials. To find out how much better than the designs then in use, she needed to do a lot of boring calculations involving finding the Moore–Penrose inverses of matrices. She needed the arithmetic to be exact, so GAP was ideal for the job; I set her up with a laptop and she could do the sums. (These designs have been published but never implemented despite their advantages: they would need to be approved by a regulator, and getting approval costs serious money; drugs companies would not pay, since this would be tantamount to admitting that their existing designs are less than perfect. So it goes.)
Neubüser was much more than just the originator of GAP: a skilled computational group theorist himself, and an inspiring teacher. Indeed, when I wrote my book on permutation groups in the late 1990s, he wrote me a long account of the trials and mis-steps in the classification of transitive subgroups of low-degree symmetric groups, and permitted me to quote it in the book (which I did).
But GAP, together with his students, make up his main legacy.