This computes the parameter test ideal of a Cohen-Macaulay ring. Technically, it computes τ(ω) : ω where ω is a canonical module and τ(ω) it the (parameter) testModule as computed by testModule. For example, the following example is F-rational and so has trivial parameter test ideal.
i1 : T = ZZ/5[x,y]; |
i2 : S = ZZ/5[a,b,c,d]; |
i3 : g = map(T, S, {x^3, x^2*y, x*y^2, y^3}); o3 : RingMap T <--- S |
i4 : R = S/(ker g); |
i5 : parameterTestIdeal(R) o5 = ideal 1 o5 : Ideal of R |
Consider now a non-F-rational Gorenstein ring where the testIdeal and parameterTestIdeal coincide.
i6 : R = ZZ/7[x,y,z]/ideal(x^3+y^3+z^3); |
i7 : parameterTestIdeal(R) o7 = ideal (z, y, x) o7 : Ideal of R |
i8 : testIdeal(R) o8 = ideal (z, y, x) o8 : Ideal of R |