If I is either an ideal or a submodule of a module M, the saturation (I : J^*) is defined to be the set of elements f in the ring (first case) or in M (second case) such that J^N * f is contained in I, for some N large enough.
For example, one way to homogenize an ideal is to homogenize the generators and then saturate with respect to the homogenizing variable.
i1 = R = ZZ/32003[a..d]
o1 = R
o1 : PolynomialRing
i2 = I = ideal(a^3-b, a^4-c)
o2 = ideal | a3-b a4-c |
o2 : Ideal
i3 = Ih = homogenize(I,d)
o3 = ideal | a3-bd2 a4-cd3 |
o3 : Ideal
i4 = saturate(Ih,d)
o4 = image | ab-cd a2c-b2d b3-ac2 a3-bd2 |
1
R - module, submodule of R
Allowable options include:
The strategy option value should be one of the following:
The computation is currently not stored anywhere: this means that the computation cannot be continued after an interrupt.. This will be changed in a later version.
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