Abstract
We present an algorithm that tests the triviality and computes the differential dimension and a parametric set for an ordinary differential polynomial ideal. No factorization is needed. The basic operation in our algorithm is the test of invertibility of an algebraic polynomial with respect to a finite set of algebraic polynomials. The algorithm has been implemented in the computer algebra system MAPLE and has been tested successfully on many examples.
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Rody, A.K., Maârouf, H. & Ssafini, M. Triviality and Dimension of a System of Algebraic Differential Equations. Journal of Automated Reasoning 20, 365–385 (1998). https://doi.org/10.1023/A:1005821729260
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DOI: https://doi.org/10.1023/A:1005821729260