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Initial ideal

InitialIdeal(I: IDEAL, Inds: LIST): IDEAL

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 II, pg.463).

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

See Also