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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 tangent 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