The method of creative telescoping
Journal of Symbolic Computation
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition
Proceedings of the 2nd GI Conference on Automata Theory and Formal Languages
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Suppose you want to find the solution S to a mathematical problem in some domain. Depending upon the type of operations under consideration that lead to the construction of a solution S, one can distinguish between "pure mathematics" (which uses tools such as infinite union, limits, etc.) and "algorithmic mathematics" (whose tools are substitution, if-then-else, recursion, etc.). Algorithmic mathematics is interested only in those solutions that can be expressed by constructs whose effects can be realized by (idealized) machines. Hence, theessence of algorithmic problem solving hinges on the algorithmic realization of solutions "relative" to given "black box" (i.e. idealized machine) operations.