Computing the Hermite Form of a Matrix of Ore Polynomials

@article{Giesbrecht2011ComputingTH,
  title={Computing the Hermite Form of a Matrix of Ore Polynomials},
  author={M. Giesbrecht and M. S. Kim},
  journal={ArXiv},
  year={2011},
  volume={abs/1109.3656}
}
  • M. Giesbrecht, M. S. Kim
  • Published 2011
  • Mathematics, Computer Science
  • ArXiv
  • Let R=F[D;sigma,delta] be the ring of Ore polynomials over a field (or skew field) F, where sigma is a automorphism of F and delta is a sigma-derivation. Given a an m by n matrix A over R, we show how to compute the Hermite form H of A and a unimodular matrix U such that UA=H. The algorithm requires a polynomial number of operations in F in terms of both the dimensions m and n, and the degree of the entries in A. When F=k(z) for some field k, it also requires time polynomial in the degree in z… CONTINUE READING
    20 Citations

    Topics from this paper

    Popov Form Computation for Matrices of Ore Polynomials
    • 4
    • Highly Influenced
    • PDF
    Computing the Maximum Degree of Minors in Skew Polynomial Matrices
    • T. Oki
    • Computer Science, Mathematics
    • ArXiv
    • 2019
    • 2
    • Highly Influenced
    Computing GCRDs of approximate differential polynomials
    • 4
    • PDF
    On Solving (Non)commutative Weighted Edmonds' Problem
    • T. Oki
    • Mathematics, Computer Science
    • ICALP
    • 2020
    • 1
    • PDF
    Computing Approximate Greatest Common Right Divisors of Differential Polynomials
    • 4
    • PDF
    On Unimodular Matrices of Difference Operators
    • 2

    References

    SHOWING 1-10 OF 45 REFERENCES
    A Polynomial-Time Algorithm for the Jacobson Form of a Matrix of Ore Polynomials
    • 5
    A polynomial-time algorithm for the Jacobson form for matrices of differential operators
    • 12
    • PDF
    On Computing the Hermite Form of a Matrix of Differential Polynomials
    • 10
    • PDF
    Computing diagonal form and Jacobson normal form of a matrix using Gröbner bases
    • 19
    • PDF
    Solving Systems of Linear Equations over Polynomials
    • R. Kannan
    • Computer Science, Mathematics
    • Theor. Comput. Sci.
    • 1985
    • 43
    Computing Popov Form of General Ore Polynomial Matrices
    • 21
    • PDF
    On fast multiplication of polynomials over arbitrary algebras
    • 279
    • PDF
    Algorithms for normal forms for matrices of polynomials and ore polynomials
    • 18
    Fraction-free row reduction of matrices of Ore polynomials
    • 72
    Exact Solution of Linear Equations Using P-Adie Expansions*
    • 111
    • Highly Influential
    • PDF