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 InitialIdeal

Initial ideal

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

 Description
Let Inds be a subset of the set of indeterminates, and let 0 be the degree of the remaining indeterminates. The initial form with respect to Inds 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 .

If Inds is the set of all indeterminates then the initial ideal is also called the tangent cone of I ( TgCone ).

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

 Example
 ```/**/ use R ::= QQ[x,y]; /**/ I := ideal(x^3 +x^2 -y^2); /**/ InitialIdeal(I, [x,y]); ideal(x^2 -y^2) /**/ TgCone(I); ideal(x^2 -y^2) /**/ use R ::= QQ[x,y]; /**/ I := ideal(x^2 +x*y); /**/ InitialIdeal(I, [x,y]); ideal(x^2 +x*y) /**/ InitialIdeal(I, [x]); ideal(x*y) ```