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Given two coprime polynomials P and Q in Z[x,y] of degree at most d and coefficients of bitsize at most τ, we address the problem of computing a triangular decomposition {(Ui(x),Vi(x,y))}i∈I of the system {P,Q}.The state-of-the-art worst-case complexities for computing such triangular decompositions when the curves defined by the input polynomials do not have common vertical asymptotes are O˜(d4)...
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