Abstract:
We investigate the connection between divisibility of full-rank square matrices of linear scalar differential operators over some differential field $K$, and the solution spaces of these matrices over the universal Picard–Vessiot extension of $K$. We establish some properties of the solution spaces of the greatest common right divisor and the least common left multiple of such matrices.
Key words:computer algebra algorithms, differential operator matrices, divisibility of square matrices of differential operators, solution space, greatest common right divisor, least common left multiple.
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