Abstract
Differential resultant formulas are defined, for a system P of n ordinary Laurent differential polynomials in n−1 differential variables. These are determinants of coefficient matrices of an extended system of polynomials obtained from P through derivations and multiplications by Laurent monomials. To start, through derivations, a system ps(P) of L polynomials in L− 1 algebraic variables is obtained, which is non sparse in the order of derivation. This enables the use of existing formulas for the computation of algebraic resultants, of the multivariate sparse algebraic polynomials in ps(P), to obtain polynomials in the differential elimination ideal generated by P. The formulas obtained are multiples of the sparse differential resultant defined by Li, Yuan and Gao, and provide order and degree bounds in terms of mixed volumes in the generic case.
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