An ideal *I* in a ring *S* is said to satisfy the condition *G _{m}* if, for every prime ideal

The command `whichGm I` returns the largest *m* such that *I* satisfies *G _{m}*, or infinity if

This condition arises frequently in work of Vasconcelos and Ulrich and their schools on Rees algebras and powers of ideals. See for example Morey, Susan; Ulrich, Bernd: Rees algebras of ideals with low codimension. Proc. Amer. Math. Soc. 124 (1996), no. 12, 3653--3661.

i1 : kk=ZZ/101; |

i2 : S=kk[a..c]; |

i3 : m=ideal vars S o3 = ideal (a, b, c) o3 : Ideal of S |

i4 : i=(ideal"a,b")*m+ideal"c3" 2 2 3 o4 = ideal (a , a*b, a*c, a*b, b , b*c, c ) o4 : Ideal of S |

i5 : whichGm i o5 = 3 |

- analyticSpread -- Compute the analytic spread of a module or ideal
- minimalReduction -- Find a minimal reduction of an ideal
- reductionNumber -- Reduction number of one ideal with respect to another

- whichGm(Ideal)