Singular points of algebraic curves
Journal of Symbolic Computation
A polynomial approach to linear algebra
A polynomial approach to linear algebra
The moving line ideal basis of planar rational curves
Computer Aided Geometric Design
Journal of Symbolic Computation
The µ-basis of a planar rational curve: properties and computation
Graphical Models
Visualisation of Implicit Algebraic Curves
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
Computing singular points of plane rational curves
Journal of Symbolic Computation
μ-Bases and singularities of rational planar curves
Computer Aided Geometric Design
On the problem of proper reparametrization for rational curves and surfaces
Computer Aided Geometric Design
Regularity criteria for the topology of algebraic curves and surfaces
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
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We prove a result similar to the conjecture of Chen et al. (2008) concerning how to calculate the parameter values corresponding to all the singularities, including the infinitely near singularities, of rational planar curves from the Smith normal forms of certain Bezout resultant matrices derived from @m-bases. A great deal of mathematical lore is hidden behind their conjecture, involving not only the classical blow-up theory of singularities from algebraic geometry, but also the intrinsic relationship between @m-bases and the singularities of rational planar curves. Here we explore these mathematical foundations in order to reveal the true nature of this conjecture. We then provide a novel approach to proving a related conjecture, which in addition to these mathematical underpinnings requires only an elementary knowledge of classical resultants.