Title :
Bracket Producing Rows and Columns of the Dixon Determinant
Author :
Xiao, Wei ; Chionh, Eng-Wee
Author_Institution :
Crimson Logic
Abstract :
The Dixon resultant for a bivariate polynomial system has many interesting properties. When the unmixed canonical bidegree monomial support of the polynomial system undergoes corner cutting, some monomial points become distinguished by being exposed. When a corner has exactly three exposed monomial points, certain rows and columns of the Dixon matrix, called almost-exposed rows and columns, produce a factor which is a power of the bracket corresponding to the three exposed points. The power is determined by the relative positions of these three exposed points. This observation is very useful when constructing quotient Dixon resultants
Keywords :
determinants; polynomial matrices; Dixon determinant; bivariate polynomial system; bracket producing columns; bracket producing rows; quotient Dixon resultants; Equations; Lattices; Logic; Polynomials; Scientific computing; Sparse matrices; Terminology;
Conference_Titel :
Symbolic and Numeric Algorithms for Scientific Computing, 2006. SYNASC '06. Eighth International Symposium on
Conference_Location :
Timisoara
Print_ISBN :
0-7695-2740-X
DOI :
10.1109/SYNASC.2006.20