The result is the ideal obtained by first extending to the localized ring and then contracting back to the original ring.
i1 : R = ZZ/(101)[x,y]; |
i2 : I = ideal (x^2,x*y); o2 : Ideal of R |
i3 : P1 = ideal (x); o3 : Ideal of R |
i4 : localize(I,P1) o4 = ideal x o4 : Ideal of R |
i5 : P2 = ideal (x,y); o5 : Ideal of R |
i6 : localize(I,P2) 2 o6 = ideal (x , x*y) o6 : Ideal of R |
i7 : R = ZZ/31991[x,y,z]; |
i8 : I = ideal(x^2,x*z,y*z); o8 : Ideal of R |
i9 : P1 = ideal(x,y); o9 : Ideal of R |
i10 : localize(I,P1) o10 = ideal (y, x) o10 : Ideal of R |
i11 : P2 = ideal(x,z); o11 : Ideal of R |
i12 : localize(I,P2) 2 o12 = ideal (z, x ) o12 : Ideal of R |
The strategy option value should be one of the following, with default value 1.
This strategy does not require the calculation of the assassinator, but can require the computation of high powers of ideals. The method appears in Eisenbud-Huneke-Vasconcelos, Invent. Math. 110 (1992) 207-235.
This strategy uses a separator polynomial - a polynomial in all of the associated primes of { t I} but { t P} and those contained in { t P}. In this strategy, the assassinator of the ideal will be recalled, or recomputed using Strategy => 1 if unknown. The separator polynomial method is described in Shimoyama-Yokoyama, J. Symbolic computation, 22(3) 247-277 (1996). This is the same as Strategy => 1 except that, if unknown, the assassinator is computed using Strategy => 2.
Authored by C. Yackel. Last modified June, 2000.
The ideal P is not checked to be prime.
The object localize is a method function with options.