Computing Kazhdan-Lusztig-Vogan Polynomials for E8

This is not a PLT paper, but I found the programming adventures of mathematicians trying to compute the Kazhdan-Lusztig polynomials for E8 very interesting: The Character Table for E8 by David Vogan. The software part begins on page 9.

I wish he had expanded on the following (emphasis mine in bold):

So late in 2004, Fokko began to add to his software an implementation of the Kazhdan-Lusztig algorithm for real groups. The papers in which this algorithm is formulated are extremely dense, and written with no consideration for computational practice. An expert could easily spend many months just to understand the mathematical statements. Fortunately, Jeff Adams had been working on a new formulation of Theorem 6 (parametrizing irreducible representations), growing out of earlier work that he did with Dan Barbasch and me. Jeff's formulation seemed suited to computer implementation; he had been working with Fokko to make it more so.

Over the course of the next year, Fokko understood the Kazhdan-Lusztig algorithm for real groups, recasting it in the language that he and Jeff had developed. He wrote clear and efficient code to implement it. In November of 2005 --incredibly soon!-- he finished. Very quickly he and Jeff used the software to compute Kazhdan-Lusztig polynomials (and so character tables) for all of the real forms of F4, E6, and E7, and for the non-split form of E8.