CASA Function: tangSpace

Compute tangent space and tangent cone.

Calling Sequence:

• B := tangSpace(A,point)
• B := tangSpace(A,point,"cone")

Parameters:

A : algset("impl")

• algebraic set in implicit representation

point : list

• point in A.

"cone" : string

• The string "cone".

Result:

B : algset

• The tangent space of the given algebraic set in the given point.

Description:

• The call tangSpace(A,point) computes an algebraic set defining the tangent space of variety A at point point. The tangent space is defined to be a set of points on all lines intersecting A at point with multiplicity bigger than 1.
• If the third optional parameter is the string "cone", then the tangent cone (set of lines generating the tangent space) is returned.

Examples:

> a1:=mkImplAlgSet([-15*y^2*z^3-76*y^3*z^2-z^5-3*y*z^4-15*x*y^2*z^2

> -11*x*y^3*z-x*z^4-3*x*y*z^3+y^3*x^2],[x,y,z],

> ["basespace"="projective"]);

> tangSpace(a1,[0,1,0]);

> tangSpace(a1,[0,1,0],"cone");

See Also: