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  • @techreport{RISC4040,
    author = {Johannes Middeke},
    title = {{ Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm}},
    language = {english},
    abstract = {We consider matrices over a ring K [∂; σ , θ] of Ore polynomials over a skew field K . Since the Popov and Hermite normal forms are both Gröbner bases (for term over position and position over term ordering resp.), the classical FGLM-algorithm provides a method of converting one into the other. In this report we investigate the exact formulation of the FGLM algorithm for not necessarily “zero-dimensional” modules and give an illustrating implementation in Maple. In an additional section, we will introduce a second notion of Gröbner bases roughly following [Pau07]. We will show that these vectorial Gröbner bases correspond to row-reduced matrices. },
    number = {10-16},
    year = {2010},
    length = {45},
    type = {RISC Report Series},
    institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
    address = {Schloss Hagenberg, 4232 Hagenberg, Austria}
    }