"Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm"
, Serie RISC Report Series, Nummer 10-16, JKU Linz, Altenberger Str. 69, 4040 Linz, Austria, 1-2010
Converting between the Popov and the Hermite form of matrices of differential operators using an FGLM-like algorithm
Sprache des Titels:
We consider matrices over a ring K [?; ? , ?] 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.