SOME CONCEPTS ABOUT THE MULTIGRADED POLYNOMIAL SYSTEMS AND THE STRUCTURE OF NEWTON POLYTOPE
Keywords:
Multigraded polynomial, Minkowski sum, Mixed volume, Newton polytopeAbstract
Finding the solutions of a system of non – linear polynomial equations has received a lot of attention since ancient times. Recent active ongoing research related to solving such equations is on the construction and implemention of the method of sparse resultant. From the work of Emiris, an effective method for constructing sparse resultant matrices.This method relies the subdivision of the Minkowski sum of the Newton polytopes of polynomial systems, which generalizes the sparse elimination theory.In addition ,the mixed cells of the mixed subdivision can be used to compute the mixed volume of the Minikowski sum of Newton polytopes .
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