“Computational Algebraic Geometry And Geometric Modeling” by Abhyankar, Bajaj and Hoffmann
Conference:
Type(s):
Entry Number: 26
Title:
- Computational Algebraic Geometry And Geometric Modeling
Organizer(s):
Presenter(s)/Author(s):
Abstract:
TOPICS
• Introduction to analytic and projective geometry
Conic sections
Points at infinity
Affine space/Projective plane
• Introduction to theory of equations
Polynomials, power series, rational functions
Completing the kth Power
Functional linear transformations
• Rudiments of algebraic geometry
Algebraic curves
Singularities for a curve
Tangents at singularities
Places of a curve-Newton’s theorem
Resolution of singularities-Quadratic transformations
Bezout’s theorem
Polynomial, rational and birational maps-Luroth’s
theorem, Castelnouvo’s Theorem
• Computing parametric equations
Efficient algorithms for low degree curves and surfaces
Genus criterion for the rationality of a curve
• Computing Implicit equations
Efficient algorithms for rational parametric curves
Extraneous factors problem for rational parametric
surfaces and algorithms for surfaces
• Computing surface-surface intersections
Numerical high order scheme for implicit-implicit and
parametric intersections
Adaptive step size selection in tracing
Algebraic methods for analyzing and handling singularities
Contents/Schedule PDF:
Contributed By:
- Mary Whitton
Location:
- Babbage Institute
