reductionNumber takes an ideal I that is homogeneous or inhomogeneous (in the latter case the ideal is to be regarded as an ideal in the localization of the polynomial ring at the origin.). It returns the integer k such that for a generic minimal reduction J of I, JIk = Ik+1.
The routine is probabilistic, since it depends on the routine minimalReduction.
i1 : kk = ZZ/101; |
i2 : S = kk[a..c]; |
i3 : m = ideal vars S; 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 : analyticSpread i o5 = 3 |
i6 : minimalReduction i Warning: minimal reduction is not necessarily homogeneous 3 2 2 3 2 o6 = ideal (50c + 42a - 41a*b - 15b + 39a*c - 22b*c, 2c + 45a + a*b + ------------------------------------------------------------------------ 2 3 2 2 19b - 39a*c - 38b*c, - 32c - 4a - 42a*b - 32b - 16a*c + 31b*c) o6 : Ideal of S |
i7 : reductionNumber i Warning: minimal reduction is not necessarily homogeneous o7 = 1 |