Publication Date
2002
Journal or Book Title
Algorithmic & Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science
Abstract
Enumerative Geometry is concerned with the number of solutions to a structured system of polynomial equations, when the structure comes from geometry. Enumerative real algebraic geometry studies real solutions to such systems, particularly a priori information on their number. Recent results in this area have, often as not, uncovered new and unexpected phenomena, and it is far from clear what to expect in general. Nevertheless, some themes are emerging. This comprehensive article describe the current state of knowledge, indicating these themes, and suggests lines of future research. In particular, it compares the state of knowledge in Enumerative Real Algebraic Geometry with what is known about real solutions to systems of sparse polynomials.
Pages
139-180
Volume
60
Book Series Title
DIMACS
Recommended Citation
Sottile, Frank, "Enumerative Real Algebraic Geometry" (2002). Algorithmic & Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science. 134.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/134
Comments
This is a pre-published version harvested from ArXiv.org. The published version can be found at http://dimacs.rutgers.edu/Volumes/Vol60.html