Software Engineering and complexity in effective Algebraic Geometry

Authors:
Joos Heintz;Bart Kuijpers;AndréS Rojas Paredes
Affiliations:
Departamento de Computación, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina and CONICET, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina an ...;Database and Theoretical Computer Science Research Group, Hasselt University, Agoralaan, Gebouw D, 3590 Diepenbeek, Belgium;Departamento de Computación, Universidad de Buenos Aires, Ciudad Universitaria, Pab. I, 1428 Buenos Aires, Argentina
Venue:
Journal of Complexity
Year:
2013

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Abstract

One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.