Software Engineering and Complexity in Effective Algebraic Geometry

Provided by: Cornell University
Topic: Software
Format: PDF
One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the last fifteen years considerable complexity progress in effective polynomial equation solving. The authors 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.

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