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TgCone

tangent cone

Syntax 
TgCone(I: IDEAL): IDEAL

Description
The initial form of a polynomial f is the homogeneous component of f of the lowest degree (in contrast with the leading form, see LF , DF ).

The initial ideal of the ideal I is the ideal generated by the initial forms of all polynomials in I . It is also called tengent cone (which strictly is the variety defined by the initial ideal).

The implementation is based on Lazard's method (see Kreuzer-Robbiano, Commutative Computer Algebra 2, pg.463).

Example 
/**/  Use R ::= QQ[x,y,z];
/**/  TgCone(ideal(x^3-y));
ideal(y)
/**/  TgCone(ideal(x^3+x^2-y^2));
ideal(x^2 -y^2)

/**/  I := ideal(x^3-y*z, y^2-x*z, z^2-x^2*y);
/**/  TgCone(I); -- same as InitialIdeal(I, [x,y,z]);
ideal(z^2, y*z, y^2 -x*z)

See Also