The BKK root count in
Authors:
T. Y. Li and Xiaoshen Wang
Journal:
Math. Comp. 65 (1996), 14771484
MSC (1991):
Primary 52B20; Secondary 65H10, 68Q40
MathSciNet review:
1370853
Fulltext PDF Free Access
Abstract 
References 
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Additional Information
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 HuberSturmfels 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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Additional Information
T. Y. Li
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 488241027
Email:
li@mth.msu.edu
Xiaoshen Wang
Affiliation:
Department of Mathematics and Computer Science, University of Central Arkansas, Conway, Arkansas 720350001
Email:
wangx@cc1.uca.edu
DOI:
http://dx.doi.org/10.1090/S0025571896007788
PII:
S 00255718(96)007788
Keywords:
BKK bound,
mixed volume,
homotopy continuation
Received by editor(s):
November 23, 1994
Received by editor(s) in revised form:
October 9, 1995
Additional Notes:
The first author’s research was supported in part by NSF under Grant DMS9504953 and by a Guggenheim Fellowship.
Article copyright:
© Copyright 1996
American Mathematical Society
