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StdBasis

Standard basis

Syntax 
StdBasis(I: IDEAL): LIST

Description
A standard basis of the ideal I is a set of polynomials whose initial forms generate the tangent cone of I (see TgCone for more details).

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

Example 
/**/  Use R ::= QQ[x,y,z];
/**/  I := ideal(x^2*z-2*y, x^3+y^2-y*z);
StdBasis(I);
[(-1/2)*x^2*z +y, (1/2)*x^2*y*z +(-1/2)*x^2*z^2 +x^3]
/**/  TgCone(I);
ideal(y, x^3)

See Also