Exact symbolic–numeric computation of planar algebraic curves
نویسندگان
چکیده
منابع مشابه
Exact symbolic-numeric computation of planar algebraic curves
We present a novel certified and complete algorithm to compute arrangements of real planar algebraic curves. It provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic curves in terms of a cylindrical algebraic decomposition. From a high-level perspective, the overall method splits into two main subroutines, namely an algorithm denoted...
متن کاملTopology and arrangement computation of semi-algebraic planar curves
We describe a new subdivision method to efficiently compute the topology and the arrangement of implicit planar curves. We emphasize that the output topology and arrangement are guaranteed to be correct. Although we focus on the implicit case, the algorithm can also treat parametric or piecewise linear curves without much additional work and no theoretical difficulties. The method isolates sing...
متن کاملExact sequences of semistable vector bundles on algebraic curves
Let X be a smooth complex projective curve of genus g ≥ 1. If g ≥ 2, assume further that X is either bielliptic or with general moduli. Fix integers r, s, a, b with r > 1, s > 1 and as ≤ br. Here we prove the existence of an exact sequence 0 → H → E → Q → 0 of semistable vector bundles onX with rk(H) = r, rk(Q) = s, deg(H) = a and deg(Q) = b.
متن کاملOn the complexity of computing with planar algebraic curves
In this paper, we give improved bounds for the computational complexity of computing with planar algebraic curves. More specifically, for arbitrary coprime polynomials f , g ∈ Z[x, y] and an arbitrary polynomial h ∈ Z[x, y], each of total degree less than n and with integer coefficients of absolute value less than 2 , we show that each of the following problems can be solved in a deterministic ...
متن کاملMultiple View Geometry of Non-planar Algebraic Curves
We introduce a number of new results in the context of multi-view geometry from general algebraic curves. We start with the derivation of the extended Kruppa’s equations which are responsible for describing the epipolar constraint of two projections of a general (non-planar) algebraic curve. As part of the derivation of those constraints we address the issue of dimension analysis and as a resul...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2013
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2013.04.014