I have spent a week, perhaps 25 hours, deriving the gravitational potential of a triangle. The results are here. The intermediate algebra is slightly messy. I am old and I make many mistakes in my algebra. By subjecting my derivations to frequent numerical tests I locate and catch my many errors. I do not now understand how I ever managed to do even more complex algebra before I had the crutch of mechanical numerical corroboration.
There remains a big problem. My algebraic skills are wrapped up in conventional mathematical notation while the mechanical numerical apparatus is Scheme. While languages such as C may be nearer to conventional mathematical notation I have found that they are not near enough. Also I need Scheme’s functional capacities.
A project suggests itself: A Scheme program to do some of these algebraic manipulations. Another project would be to transcribe the Wolfram’s textual form of the integral to a Scheme expression.
My friend Gabriel Laddel who runs Macsyma, provides this much simpler result!