We are looking for the most efficient (most recent, or best) techniques to check if two algebraic expressions (elementary, Calculus-type functions) are equivalent (or if an expression is equivalent to zero, which is the so-called "zero-equivalence" problem). So far we came across two papers that seem to be relatively easy to implement:

"Determining the equivalence of algebraic expressions by hash coding" by William Martin, 1971

and

"Determining equivalence of expressions in random polynomial time" by Gaston Gonnet, 1984

but both are not easy to read and it seems like there are many details missing.

Here is the question: is there any more recent research in this direction? Maybe, a book or a paper which is more accessible?

Best, Denis