Sparse Differential Resultant for Laurent Differential Polynomials

Linear sparse differential resultant formulas

Let P be a system of n linear nonhomogeneous generic sparse ordinary differential polynomials in n − 1 differential indeterminates. In this paper, differential resultant formulas are presented to compute, whenever it exists, the sparse differential resultant ∂Res(P) introduced by Li, Gao and Yuan in [12], as the determinant of the coefficient matrix of an appropriate set of derivatives of diffe...

Hybrid Sparse Resultant Matrices for Bivariate Polynomials

We study systems of three bivariate polynomials whose Newton polygons are scaled copies of a single polygon. Our main contribution is to construct square resultant matrices, which are submatrices of those introduced by Cattani et al. (1998), and whose determinants are nontrivial multiples of the sparse (or toric) resultant. The matrix is hybrid in that it contains a submatrix of Sylvester type ...

Matrix Formulae of Differential Resultant for First Order Generic Ordinary Differential Polynomials

In this paper, a matrix representation for the differential resultant of two generic ordinary differential polynomials f1 and f2 in the differential indeterminate y with order one and arbitrary degree is given. That is, a non-singular matrix is constructed such that its determinant contains the differential resultant as a factor. Furthermore, the algebraic sparse resultant of f1, f2, δf1, δf2 t...

Fractional differential equations with Legendre polynomials

Sparse Resultant of Composed Polynomials IMixed-. Unmixed Case

The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1, . . . , fn be homogeneous sparse polynomials in the variables y1, . . . , yn and g1, . . . , gn be homogeneous sparse polynomials in the variables x1, . . . , xn. Let fi ◦ (g1, . . . , gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj . Naturally a quest...