Автор:Daniel Cabarcas Jaramillo Год: 2013 Издание:Scholars' Press Страниц: 108 ISBN: 9783639514926 Grobner bases are the single most important tool in applicable algebraic geometry. This is in part because they can be used to solve systems of polynomial equations. Applications in science and technology are abundant, particularly in cryptography and coding theory. Grobner bases computation is challenging and a great deal of effort has been devoted to improve algorithms to compute faster larger bases. The concept of mutant polynomials, introduced by Ding in 2006, characterizes a phenomenon of degeneration in the process of Grobner bases computation. Exploiting the appearance of mutant polynomials has led to significant improvements in Grobner bases Computation. In this work we describe several such improvements and we establish some theoretical results for mutant polynomials. We also propose LASyz, a method to avoid redundant computation in Grobner bases computation that is compatible with mutant algorithms. This is achieved by simple linear algebra procedures used to compute...
