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- Acnode abstract "An acnode is an isolated point not on a curve, but whose coordinates satisfy the equation of the curve. The term "isolated point" or "hermit point" is an equivalent term.Acnodes commonly occur when studying algebraic curves over fields which are not algebraically closed, defined as the zero set of a polynomial of two variables. For example the equationhas an acnode at the origin of , because it is equivalent toand is non-negative when ≥ 1 and when . Thus, over the real numbers the equation has no solutions for except for (0, 0).In contrast, over the complex numbers the origin is not isolated since square roots of negative real numbers exist.An acnode is a singularity of the function, where both partial derivatives and vanish. Further the Hessian matrix of second derivatives will be positive definite or negative definite. Hence the function has a local minimum or a local maximum.".
- Acnode thumbnail Isolated-point.svg?width=300.
- Acnode wikiPageID "3090256".
- Acnode wikiPageRevisionID "542431905".
- Acnode hasPhotoCollection Acnode.
- Acnode subject Category:Algebraic_curves.
- Acnode subject Category:Curves.
- Acnode subject Category:Singularity_theory.
- Acnode type Abstraction100002137.
- Acnode type AlgebraicCurves.
- Acnode type Attribute100024264.
- Acnode type Curve113867641.
- Acnode type Curves.
- Acnode type Line113863771.
- Acnode type Shape100027807.
- Acnode comment "An acnode is an isolated point not on a curve, but whose coordinates satisfy the equation of the curve. The term "isolated point" or "hermit point" is an equivalent term.Acnodes commonly occur when studying algebraic curves over fields which are not algebraically closed, defined as the zero set of a polynomial of two variables. For example the equationhas an acnode at the origin of , because it is equivalent toand is non-negative when ≥ 1 and when .".
- Acnode label "Acnode".
- Acnode label "孤立点".
- Acnode sameAs m.08qrkt.
- Acnode sameAs Q844451.
- Acnode sameAs Q844451.
- Acnode sameAs Acnode.
- Acnode wasDerivedFrom Acnode?oldid=542431905.
- Acnode depiction Isolated-point.svg.
- Acnode isPrimaryTopicOf Acnode.
