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CC
2010
Springer
135views System Software» more  CC 2010»
13 years 7 months ago
Counting Irreducible Components of Complex Algebraic Varieties
Abstract. We present an algorithm for counting the irreducible components of a complex algebraic variety defined by a fixed number of polynomials encoded as straight-line programs ...
Peter Bürgisser, Peter Scheiblechner
COMPGEOM
1994
ACM
13 years 11 months ago
Almost Tight Upper Bounds for the Single Cell and Zone Problems in Three Dimensions
We consider the problem of bounding the combinatorial complexity of a single cell in an arrangement of n low-degree algebraic surface patches in 3-space. We show that this complex...
Dan Halperin, Micha Sharir
COMPGEOM
2005
ACM
13 years 9 months ago
On the exact computation of the topology of real algebraic curves
We consider the problem of computing a representation of the plane graph induced by one (or more) algebraic curves in the real plane. We make no assumptions about the curves, in p...
Raimund Seidel, Nicola Wolpert
CSJM
2008
88views more  CSJM 2008»
13 years 7 months ago
A zero-dimensional approach to compute real radicals
The notion of real radicals is a fundamental tool in Real Algebraic Geometry. It takes the role of the radical ideal in Complex Algebraic Geometry. In this article I shall describ...
Silke J. Spang
COMPGEOM
2001
ACM
13 years 11 months ago
PRECISE: efficient multiprecision evaluation of algebraic roots and predicates for reliable geometric computation
: Many geometric problems like generalized Voronoi diagrams, medial axis computations and boundary evaluation involve computation and manipulation of non-linear algebraic primitive...
Shankar Krishnan, Mark Foskey, Tim Culver, John Ke...