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Normal and triangular determinantal representations of multivariate polynomials. (English) Zbl 1420.13064

Author’s abstract: We present a new and simple algorithm for writing any multivariate polynomial in a new representation defined as a normal determinantal representation in which each entry has the form \(a_i x_i + b_i\) and the same variable appears in each column. We apply this algorithm to obtain the triangular, reduced, and uniform determinantal representations of any multivariate polynomial. The proposed algorithm could be useful also for obtaining smaller representations than those currently available for solving numerical problems.

MSC:

13P15 Solving polynomial systems; resultants
65H04 Numerical computation of roots of polynomial equations
65F50 Computational methods for sparse matrices
11C20 Matrices, determinants in number theory
15B36 Matrices of integers
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