[pkelchte]

Always wanted to see something like this! Hope it'll get referenced a lot on resources like Mathworld or Wikipedia. Love the extensiveness!

Dumb question maybe, but is knowledge like this often used in symbolic solver software? If so, would it be useful to implement examples in a programming language like Gerald Sussman did in Structure and Interpretation of Classical Mechanics?

[alexbock]

I've been working on a symbolic solver lately and have had to implement a lot of techniques manually. I'm not aware of any machine-readable database of solving techniques (which would be great for this, especially for integrals, because right now my code doesn't know any integration techniques that I don't know myself).

A lot of big solvers use algorithms[0] that can't always be reduced into a reasonable series of steps for producing nice step-by-step output, which is why e.g. Wolfram Alpha will occasionally manage to symbolically integrate something but tells you that a step-by-step solution is unavailable. (This happens even with plain algebra; Wolfram Alpha can explain how to derive the quadratic equation but not the cubic.)

Could you elaborate more on the nature of the examples from this book for those of us who haven't read it?

[0] Risch algorithm, Gaussian elimination, etc.