Linear sparse differential resultant formulas

Abstract Let P be a system of n linear nonhomogeneous ordinary differential polynomials in a set U of n − 1 differential indeterminates. Differential resultant formulas are presented to eliminate the differential indeterminates in U from P . These formulas are determinants of coefficient matrices of appropriate sets of derivatives of the differential polynomials in P , or in a linear perturbation P e of P . In particular, the formula ∂ FRes ( P ) is the determinant of a matrix M ( P ) having no zero columns if the system P is “super essential”. As an application, if the system P is sparse generic, such formulas can be used to compute the differential resultant ∂ Res ( P ) introduced by Li et al. (2011) [19] .

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