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I've always wondered about the Risch "algorithm". It's not really an algorithm because at one crucial step it says "determine if this expression is zero" which
by jordigh 10y ago
I've always wondered about the Risch "algorithm". It's not really an algorithm because at one crucial step it says "determine if this expression is zero" which is essentially an open problem. What is it that Axiom does? Does it find antiderivatives where others fail?
- thechao 10y agoThe Risch "algorithm", in this sense, is an implementation of the Risch decision procedure; in particular, the Risch-Bronstein-Trager algorithm. Axiom's version was written, in large part, by Bronstein, himself. Axiom's implementation is complete in the sense of capturing the entire Risch decision procedure for elementary functions: it either returns the antiderivative or returns a proof that no such antiderivative exists. However, while elementary functions are extremely important, they aren't the whole story for functions; in that sense, Axiom is far weaker than, say, Mathematica.