Mathematics – Algebraic Geometry
Scientific paper
2000-07-24
Computations in Algebraic Geometry with Macaulay 2, edited by D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels. ACM 8, S
Mathematics
Algebraic Geometry
LaTeX 2e, 22 pages, 1 .eps figure. Source file (.tar.gz) includes Macaulay 2 code in article, as well as Macaulay 2 package re
Scientific paper
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration. We use Macaulay 2 to investigate some problems from enumerative geometry, illustrating some applications of symbolic computation to this important problem of solving systems of polynomial equations. Besides enumerating solutions to the resulting polynomial systems, which include overdetermined, deficient, and improper systems, we address the important question of real solutions to these geometric problems. The text contains evaluated Macaulay 2 code to illuminate the discussion. This is a chapter in the forthcoming book "Computations in Algebraic Geometry with Macaulay 2", edited by D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels. While this chapter is largely expository, the results in the last section concerning lines tangent to quadrics are new.
No associations
LandOfFree
An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2 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 An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2 will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-106414