# maxGs -- maximum G_s of a monomial ideal

## Synopsis

• Usage:
d = maxGs I
• Inputs:
• I, ,
• Outputs:
• d, an integer, the maximum value of s such that I has property G_s (possibly infinity).

## Description

Recall that an ideal I has the property G_s if, for every prime P with codim P <s, the localization I_P is generated by at most codim P elements. For example, if s = codim I, then I is G_s iff I is generically a complete intersection.

 i1 : R = QQ[x_1,x_2,x_3]; i2 : I = monomialIdeal(x_1^2,x_1*x_2,x_1*x_3,x_2^2,x_2*x_3); o2 : MonomialIdeal of R i3 : maxGs(I) o3 = 3