TangentPlane - Maple Help

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RegularChains[AlgebraicGeometryTools]

  

TangentPlane

  

compute the plane plane of an hypersurface at a point given by a regular chain

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

TangentPlane(rc, f, R)

Parameters

R

-

polynomial ring

rc

-

regular chain of R

f

-

a polynomial of R

Description

• 

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](..).

Examples

withRegularChains:withChainTools:withAlgebraicGeometryTools:

RPolynomialRingx,y,z

Rpolynomial_ring

(1)

rcEmptyR

rcregular_chain

(2)

rcChainz1,y,x,rc,R

rcregular_chain

(3)

Equationsrc,R

x,y,z1

(4)

fxz+zy+yx

fyx+xz+zy

(5)

tpTangentPlanerc,f,R

tp_x+_y,rc

(6)

Compatibility

• 

The RegularChains[AlgebraicGeometryTools][TangentPlane] command was introduced in Maple 2020.

• 

For more information on Maple 2020 changes, see Updates in Maple 2020.

See Also

Chain

Empty

Equations

PolynomialRing

RegularChains