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Fast Computation of Shifted Popov Forms of Polynomial Matrices via Systems of Modular Polynomial Equations
2016
Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16
We give a Las Vegas algorithm which computes the shifted Popov form of an m × m nonsingular polynomial matrix of degree d in expected O(m^ω d) field operations, where ω is the exponent of matrix multiplication and O(·) indicates that logarithmic factors are omitted. This is the first algorithm in O(m^ω d) for shifted row reduction with arbitrary shifts. Using partial linearization, we reduce the problem to the case d <σ/m where σ is the generic determinant bound, with σ / m bounded from above
doi:10.1145/2930889.2930936
dblp:conf/issac/Neiger16
fatcat:zv6bihlnh5f4pgtyfb27pflk5y