Details:
Title  A concise proof of the Kronecker polynomial system solver from scratch  Author(s)  Clémence Durvye, Gregoire Lecerf  Type  Article in Journal  Abstract  Nowadays polynomial system solvers are involved in sophisticated computations in algebraic geometry as well as in practical engineering. The most popular algorithms are based on Gröbner bases, resultants, Macaulay matrices, or triangular decompositions. In all these algorithms, multivariate polynomials are expanded in a monomial basis, and the computations mainly reduce to linear algebra. The major drawback of these techniques is the exponential explosion of the size of the polynomials needed to represent highly positive dimensional solution sets. Alternatively, the “Kronecker solver” uses data structures to represent the input polynomials as the functions that compute their values at any given point. In this paper, we present the first selfcontained and student friendly version of the Kronecker solver, with a substantially simplified proof of correctness. In addition, we enhance the solver in order to compute the multiplicities of the zeros without any extra cost.  Keywords  Polynomial system solving, Elimination theory, Algorithm, Complexity  ISSN  07230869 
URL 
http://www.sciencedirect.com/science/article/pii/S072308690700045X 
Language  English  Journal  Expositiones Mathematicae  Volume  26  Number  2  Pages  101  139  Year  2008  Edition  0  Translation 
No  Refereed 
No 
