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PG
2007
IEEE
14 years 1 months ago
Visualisation of Implicit Algebraic Curves
We describe a new algorithm for the visualisation of implicit algebraic curves, which isolates the singular points, compute the topological degree around these points in order to ...
Lionel Alberti, Bernard Mourrain
ISSAC
2004
Springer
67views Mathematics» more  ISSAC 2004»
14 years 23 days ago
Rational general solutions of algebraic ordinary differential equations
We give a necessary and sufficient condition for an algebraic ODE to have a rational type general solution. For an autonomous first order ODE, we give an algorithm to compute a r...
Ruyong Feng, Xiao-Shan Gao
JSC
2008
126views more  JSC 2008»
13 years 5 months ago
Computing 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 -basis of the curve. It is shown that singularity...
Falai Chen, Wenping Wang, Yang Liu
COMPGEOM
1989
ACM
13 years 11 months ago
Computing the Irreducible Real Factors and Components of an Algebraic Curve
We present algorithms that decompose an algebraic curve with rational coefficients in its defining bivariate equation into its irreducible real factors and its non-empty irreducib...
Erich Kaltofen
GMP
2006
IEEE
131views Solid Modeling» more  GMP 2006»
14 years 1 months ago
Least-Squares Approximation by Pythagorean Hodograph Spline Curves Via an Evolution Process
The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. In order to solve this highly non-linear problem, we ...
Martin Aigner, Zbynek Sír, Bert Jüttle...