Factoring multivariate polynomials over algebraic number fields
SIAM Journal on Computing
Counting curves and their projections
Computational Complexity
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Journal of Symbolic Computation
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Factoring multivariate polynomials via partial differential equations
Mathematics of Computation
Modern Computer Algebra
On the complexity of factoring bivariate supersparse (Lacunary) polynomials
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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Journal of Symbolic Computation
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Proceedings of the 36th international symposium on Symbolic and algebraic computation
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CCC '11 Proceedings of the 2011 IEEE 26th Annual Conference on Computational Complexity
Detecting lacunary perfect powers and computing their roots
Journal of Symbolic Computation
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Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Factoring bivariate lacunary polynomials without heights
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Factoring bivariate lacunary polynomials without heights
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We present an algorithm which computes the multilinear factors of bivariate lacunary polynomials. It is based on a new Gap theorem which allows to test whether P(X)=∑kj=1 αjXαj(1+X)βjis identically zero in polynomial time. The algorithm we obtain is more elementary than the one by Kaltofen and Koiran (ISSAC'05) since it relies on the valuation of polynomials of the previous form instead of the height of the coefficients. As a result, it can be used to find some linear factors of bivariate lacunary polynomials over a field of large finite characteristic in probabilistic polynomial time.