Abstract
This work is limited to the zero-dimensional, radical, and bivariate case. A lexicographical Grobner basis can be simply viewed as Lagrange interpolation polynomials. In the same way the Chinese remaindering theorem generalizes Lagrange interpolation, we show how a triangular decomposition is linked to a specific Grobner basis (not the reduced one). A bound on the size of the coefficients of this specific Grobner basis is proved using height theory, then a bound is deduced for the reduced Grobner basis. Besides, the link revealed between the Grobner basis and the triangular decomposition gives straightforwardly a numerical estimate to help finding a lucky prime in the context of modular methods.
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