On the complexity of some birational transformations

Details On the complexity of some birational transformations On the complexity of some birational transformations

2005-03-31

arxiv.org/abs/math-ph/0503074v1

Journal of Physics A Mathematical and Theoretical 39 (2006) 3641

Physics

Mathematical Physics

Scientific paper

10.1088/0305-4470/39/14/009

Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions.

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