Details:
Title  Multihomogeneous resultant formulae for systems with scaled support  Author(s)  Ioannis Z. Emiris, Angelos Mantzaflaris  Type  Article in Journal  Abstract  Constructive methods for matrices of multihomogeneous (or multigraded) resultants for unmixed systems have been studied by Weyman, Zelevinsky, Sturmfels, Dickenstein and Emiris. We generalize these constructions to mixed systems, whose Newton polytopes are scaled copies of one polytope, thus taking a step towards systems with arbitrary supports. First, we specify matrices whose determinant equals the resultant and characterize the systems that admit such formulae. Bézouttype determinantal formulae do not exist, but we describe all possible Sylvestertype and hybrid formulae. We establish tight bounds for all corresponding degree vectors, and specify domains that will surely contain such vectors; the latter are new even for the unmixed case. Second, we make use of multiplication tables and strong duality theory to specify resultant matrices explicitly, for a general scaled system, thus including unmixed systems. The encountered matrices are classified; these include a new type of Sylvestertype matrix as well as Bézouttype matrices, known as partial Bezoutians. Our publicdomain Maple implementation includes efficient storage of complexes in memory, and construction of resultant matrices.  Keywords  Multihomogeneous system, Resultant matrix, Sylvester, Bézout, Determinantal formula, Maple implementation  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717111002021 
Language  English  Journal  Journal of Symbolic Computation  Volume  47  Number  7  Pages  820  842  Year  2012  Note  International Symposium on Symbolic and Algebraic Computation (ISSAC 2009)  Edition  0  Translation 
No  Refereed 
No 
