论文信息 - Computing Popov Form of General Ore Polynomial Matrices

Computing Popov Form of General Ore Polynomial Matrices

The computation of the Popov form of Ore polynomial matrices is formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended to Ore polynomial matrices in this paper. This in turn allows nullspace algorithms to be used in Popov form computations. Fraction-free and modular algorithms for nullspace computation can be used in exact arithmetic setting where coefficient growth is a concern. When specialized to ordinary polynomial matrices, our results simplify the proofs for the computation of Popov form while keeping the same worst case complexity.

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