An ideal I in a ring S is said to satisfy the condition Gm if, for every prime ideal P of codimension 0<k<m, the ideal IP in SP can be generated by at most k elements.
The call whichGm I returns the largest m such that I satisfies Gm, or infinity if I satisfies Gm for every m.
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 |