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Factoring bivariate sparse (lacunary) polynomials
 J. Complexity
"... Abstract. We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K[x,y] over an algebraic number field K and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in d. Mo ..."
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Cited by 13 (2 self)
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Abstract. We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K[x,y] over an algebraic number field K and their multiplicities, whose running time is polynomial in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over Q of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d.
Geometric lower bounds for the normalized height of hypersurfaces
, 2006
"... We are here concerned in the Bogomolov’s problem for the hypersurfaces; we give a geometric lower bound for the height of a hypersurface of G n m (i.e. without condition on the field of definition of the hypersurface) which is not a translate of an algebraic subgroup of G n m. This is an analogue of ..."
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Cited by 2 (0 self)
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We are here concerned in the Bogomolov’s problem for the hypersurfaces; we give a geometric lower bound for the height of a hypersurface of G n m (i.e. without condition on the field of definition of the hypersurface) which is not a translate of an algebraic subgroup of G n m. This is an analogue of a result of F. Amoroso and S. David who give a lower bound for the height of nontorsion hypersurfaces defined and irreducible over the rationals.