Complexity of Computations with Pfaffian and Noetherian Functions

  title={Complexity of Computations with Pfaffian and Noetherian Functions},
  author={Andrei Gabrielov and Nicolai Vorobjov},
This paper is a survey of the upper bounds on the complexity of basic algebraic and geometric operations with Pfaffian and Noetherian functions, and with sets definable by these functions. Among other results, we consider bounds on Betti numbers of sub-Pfaffian sets, multiplicities of Pfaffian intersections, effective Lojasiewicz inequality for Pfaffian functions, computing the frontier and closure of restricted semi-Pfaffian sets, constructing smooth stratifications and cylindrical cell… CONTINUE READING
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