On the Complexity Exponent of Polynomial System Solving
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 polyn...
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| Veröffentlicht in: | Foundations of computational mathematics 2021-02, Vol.21 (1), p.1-57 |
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| container_title | Foundations of computational mathematics |
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| creator | van der Hoeven, Joris Lecerf, Grégoire |
| description | 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. |
| doi_str_mv | 10.1007/s10208-020-09453-0 |
| format | Article |
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| subjects | Algorithms Applications of Mathematics Complexity Computational Complexity Computer Science Economics Fields (mathematics) Linear and Multilinear Algebras Math Applications in Computer Science Mathematics Mathematics and Statistics Matrix Theory Numerical Analysis Polynomials Rings and Algebras Symbolic Computation |
| title | On the Complexity Exponent of Polynomial System Solving |
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