Title  Numerical algorithms for dual bases of positivedimensional ideals. 
Author(s)  Krone Robert 
Type  Article in Journal 
Abstract  An ideal of a local polynomial ring can be described by calculating a standard basis with respect to a local monomial ordering. However the usual standard basis algorithms are not numerically stable. A numerically stable approach to describing the ideal is by finding the space of dual functionals that annihilate it, which reduces the problem to one of linear algebra. There are several known algorithms for finding the truncated dual up to any specified degree, which is useful for describing zerodimensional ideals. We present a stopping criterion for positivedimensional cases based on homogenization that guarantees all generators of the initial monomial ideal are found. This has applications for calculating Hilbert functions.

Keywords  Numerical algebraic geometry; computational algebraic geometry; Hilbert function; Macaulay dual space; Macaulay2 
ISSN  02194988 
URL 
http://www.worldscientific.com/doi/abs/10.1142/S0219498813500187 
Language  English 
Journal  J. Algebra Appl. 
Volume  12 
Number  6 
Pages  1350018, 21 
Publisher  World Scientific, Singapore 
Year  2013 
Edition  0 
Translation 
No 
Refereed 
No 