Mathematics – Algebraic Geometry
Scientific paper
1999-04-24
Experimental Mathematics, 9, Number 2, (2000), pp. 161-182.
Mathematics
Algebraic Geometry
30 pages, Documentation of the calculations available at http://www.math.wisc.edu/~sottile/pages/shapiro/index.html
Scientific paper
Boris Shapiro and Michael Shapiro have a conjecture concerning the Schubert calculus and real enumerative geometry and which would give infinitely many families of zero-dimensional systems of real polynomials (including families of overdetermined systems)--all of whose solutions are real. It has connections to the pole placement problem in linear systems theory and to totally positive matrices. We give compelling computational evidence for its validity, prove it for infinitely many families of enumerative problems, show how a simple version implies more general versions, and present a counterexample to a general version of their conjecture.
No associations
LandOfFree
Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Real Schubert Calculus: Polynomial systems and a conjecture of Shapiro and Shapiro will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-299241