@article{LabahnNeigerZhou:JoC:2017,
    Abstract = {Given a nonsingular n×n matrix of univariate polynomials over a field K, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use O˜(n{$\omega$}⌈s⌉) operations in K, where s is bounded from above by both the average of the degrees of the rows and that of the columns of the matrix and {$\omega$} is the exponent of matrix multiplication. The soft-O notation indicates that logarithmic factors in the big-O are omitted while the ceiling function indicates that the cost is O˜(n{$\omega$}) when s=o(1). Our algorithms are based on a fast and deterministic triangularization method for computing the diagonal entries of the Hermite form of a nonsingular matrix.},
    Author = {Labahn, George and Neiger, Vincent and Zhou, Wei},
    File = {Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix - determinant\_hermite\_polmat - a - w.pdf},
    ISSN = {0885-064X},
    Journal = {Journal of Complexity},
    Keywords = {Hermite normal form, Determinant, Polynomial matrix},
    Pages = {44--71},
    Title = {Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix},
    URL = {http://www.sciencedirect.com/science/article/pii/S0885064X17300432},
    Volume = {42},
    Year = {2017},
    bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0885064X17300432},
    bdsk-url-2 = {https://doi.org/10.1016/j.jco.2017.03.003},
    date-added = {2020-09-29 16:27:01 +0200},
    date-modified = {2020-09-29 16:27:01 +0200},
    doi = {10.1016/j.jco.2017.03.003}
}

@article{LabahnNeigerZhou:JoC:2017, Abstract = {Given a nonsingular n×n matrix of univariate polynomials over a field K, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use O˜(n{$\omega$}⌈s⌉) operations in K, where s is bounded from above by both the average of the degrees of the rows and that of the columns of the matrix and {$\omega$} is the exponent of matrix multiplication. The soft-O notation indicates that logarithmic factors in the big-O are omitted while the ceiling function indicates that the cost is O˜(n{$\omega$}) when s=o(1). Our algorithms are based on a fast and deterministic triangularization method for computing the diagonal entries of the Hermite form of a nonsingular matrix.}, Author = {Labahn, George and Neiger, Vincent and Zhou, Wei}, File = {Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix - determinant_hermite_polmat - a - w.pdf}, ISSN = {0885-064X}, Journal = {Journal of Complexity}, Keywords = {Hermite normal form, Determinant, Polynomial matrix}, Pages = {44--71}, Title = {Fast, deterministic computation of the Hermite normal form and determinant of a polynomial matrix}, URL = {http://www.sciencedirect.com/science/article/pii/S0885064X17300432}, Volume = {42}, Year = {2017}, bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0885064X17300432}, bdsk-url-2 = {https://doi.org/10.1016/j.jco.2017.03.003}, date-added = {2020-09-29 16:27:01 +0200}, date-modified = {2020-09-29 16:27:01 +0200}, doi = {10.1016/j.jco.2017.03.003} }