@article{hong_minimair_2002, title={Sparse resultant of composed polynomials I* mixed-unmixed case}, volume={33}, ISSN={["0747-7171"]}, url={http://dx.doi.org/10.1006/jsco.2001.0516}, DOI={10.1006/jsco.2001.0516}, abstractNote={The main question of this paper is: What happens to sparse resultants under composition? More precisely, let f1,…, fnbe homogeneous sparse polynomials in the variables y1,…, yn and g1,…, gn be homogeneous sparse polynomials in the variables x1,…,xn. Let fiο(g1,…,gn) be the sparse homogeneous polynomial obtained from fi by replacing yj by gj. Naturally a question arises: Is the sparse resultant of f1ο(g1,…,gn),…,f n(g1,…,gn) in any way related to the (sparse) resultants of f1,…,fn and g1,…,gn? The main contribution of this paper is to provide an answer for the case when g1,…,gn are unmixed, namely, Resc1,…,cn (f1 ο (g1,…,gn),…,fn ο (g1,…,gn)) = Resd1,…,dn (f1,…,fn)Vol(Q)ResB(g1) where Resd1,…,dn stands for the dense (Macaulay) resultant with respect to the total degrees di of the fi's, B stands for the unmixed sparse resultant with respect to the support B of the gj's,ResC1,…,Cn stands for the mixed sparse resultant with respect to the naturally induced supports Ci of the fi ο(g1,…,gn)'s, and Vol(Q) for the normalized volume of the Newton polytope of the gj. The above expression can be applied to compute sparse resultants of composed polynomials with improved efficience.}, number={4}, journal={JOURNAL OF SYMBOLIC COMPUTATION}, publisher={Elsevier BV}, author={Hong, H and Minimair, M}, year={2002}, month={Apr}, pages={447–465} } @article{minimair_2002, title={Sparse resultant of composed polynomials II unmixed-mixed case}, volume={33}, number={4}, journal={Journal of Symbolic Computation}, author={Minimair, M.}, year={2002}, pages={467–478} }