The singular points of analytic space-curves
نویسندگان
چکیده
منابع مشابه
5 Local Parametrization of Space Curves at Singular Points
We propose a symbolic computation algorithm for computing local parametrization of analytic branches and real analytic branches of a curve in n-dimensional space, which is de ned by implicit polynomial equations. The algorithm can be used in space curve tracing near a singular point, as an alternative to symbolic computations based on resolutions of singularities.
متن کاملSingular Points of Plane Curves
ly isomorphic to (C×)r−1 × (C), and hence also to (S1)r−1 × (R), where r = |J | is the number of branches and k = δ(C)− r+1 = 1 2 (μ(C) + 1 − r). The construction of the Jacobian variety J(C̃) of the non-singular curve C̃ in the large is standard in algebraic geometry. There is also a notion of Jacobian of a singular curve C , defined e.g. in [85], which, like the other, is an abelian group. Ther...
متن کاملAnalytic order of singular and critical points
We deal with the following closely related problems: (i) For a germ of a reduced plane analytic curve, what is the minimal degree of an algebraic curve with a singular point analytically equivalent (isomorphic) to the given one? (ii) For a germ of a holomorphic function in two variables with an isolated critical point, what is the minimal degree of a polynomial, equivalent to the given function...
متن کاملComputing singular points of plane rational curves
We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...
متن کاملSingular Curves in the Joint Space and Cusp Points of 3-RPR parallel manipulators
This paper investigates the singular curves in the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it...
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: Transactions of the American Mathematical Society
سال: 1929
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1929-1501473-5