Abstract
Systems of linear ordinary differential equations of arbitrary orders of full rank are considered. We study the change in the dimension of the solution space that occurs while differentiating one of the equations. Basing on this, we show a way to compute the dimension of the solution space of a given full rank system. In addition, we show how the change in the dimension can be used to estimate the number of steps of some algorithms to convert a given full rank system into an appropriate form.
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Abramov, S.A., Barkatou, M.A. (2013). On the Dimension of Solution Spaces of Full Rank Linear Differential Systems. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2013. Lecture Notes in Computer Science, vol 8136. Springer, Cham. https://doi.org/10.1007/978-3-319-02297-0_1
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DOI: https://doi.org/10.1007/978-3-319-02297-0_1
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