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 matri- ces, 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 and an additional row express- ing the toric Jacobian. If we restrict our attention to matrices of(almost)Sylvester-type and systems as specified above, then the algorithm yields the smallest possible matrix in general.
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