reductionNumber takes a pair of ideals I,J, 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.). The ideal J must be a reduction of I (that is, J⊂I and I is integrally dependent on J. This condition is checked by the function isReduction (missing documentation). It returns the smallest integer k such that JIk = Ik+1.
i1 : setRandomSeed() |
i2 : kk = ZZ/101; |
i3 : S = kk[a..c]; |
i4 : m = ideal vars S; o4 : Ideal of S |
i5 : i = (ideal"a,b")*m+ideal"c3" 2 2 3 o5 = ideal (a , a*b, a*c, a*b, b , b*c, c ) o5 : Ideal of S |
i6 : analyticSpread i o6 = 3 |
i7 : j=minimalReduction i 3 2 2 3 2 o7 = 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) o7 : Ideal of S |
i8 : reductionNumber (i,j) o8 = 1 |