The BKK root count in |
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Authors: | T Y Li Xiaoshen Wang |
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Institution: | Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027 ; Department of Mathematics and Computer Science, University of Central Arkansas, Conway, Arkansas 72035-0001 |
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Abstract: | The root count developed by Bernshtein, Kushnirenko and Khovanskii only counts the number of isolated zeros of a polynomial system in the algebraic torus . In this paper, we modify this bound slightly so that it counts the number of isolated zeros in . Our bound is, apparently, significantly sharper than the recent root counts found by Rojas and in many cases easier to compute. As a consequence of our result, the Huber-Sturmfels homotopy for finding all the isolated zeros of a polynomial system in can be slightly modified to obtain all the isolated zeros in . |
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Keywords: | BKK bound mixed volume homotopy continuation |
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