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We present a probabilistic Las Vegas algorithm for solving sufficiently generic square polynomial systems over finite fields. We achieve a nearly quadratic running time in the number of solutions, for… Click to show full abstract
We present a probabilistic Las Vegas algorithm for solving sufficiently generic square polynomial systems over finite fields. We achieve a nearly quadratic running time in the number of solutions, for densely represented input polynomials. We also prove a nearly linear bit complexity bound for polynomial systems with rational coefficients. Our results are obtained using the combination of the Kronecker solver and a new improved algorithm for fast multivariate modular composition.
Keywords:
complexity exponent;
exponent polynomial;
polynomial system;
complexity;
system solving
Journal Title: Foundations of Computational Mathematics
Year Published: 2021
Link to full text (if available)
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Journal Title: Foundations of Computational Mathematics
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!