compute the plane plane of an hypersurface at a point given by a regular chain
TangentPlane(rc, f, R)
regular chain of R
a polynomial of R
The command TangentPlane(rc, f, R) returns the tangent plane of the hypersurface defined by f at every point of F defined by rc.
The result is a list of pairs [g,ts] where ts is a zero-dimensional regular chain the zero set of which is contained in that g, and g a polynomial the zero set of which defines the tangent plane of f at ts.
It is assumed that rc is a zero-dimensional regular chain.
It is assumed that the hypersurface defined by f is non-singular at every point defined by rc.
This command is part of the RegularChains[AlgebraicGeometryTools] package, so it can be used in the form TangentPlane(..) only after executing the command with(RegularChains[AlgebraicGeometryTools]). However, it can always be accessed through the long form of the command by using RegularChains[AlgebraicGeometryTools][TangentPlane](..).
R ≔ PolynomialRing⁡x,y,z
rc ≔ Empty⁡R
rc ≔ Chain⁡z−1,y,x,rc,R
f ≔ x⁢z+z⁢y+y⁢x
tp ≔ TangentPlane⁡rc,f,R
The RegularChains[AlgebraicGeometryTools][TangentPlane] command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
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