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parameterTestIdeal -- compute the parameter test ideal of a Cohen-Macaulay ring



This function computes the parameter test ideal of a Cohen-Macaulay ring $R$. Technically, it computes \tau($\omega$) : $\omega$ where $\omega$ is a canonical module of $R$, and \tau($\omega$) is the (parameter) test module, as computed by testModule. For example, the ring $R$ in the following example is $F$-rational, and so its parameter test ideal is the unit 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, whose test ideal and parameter test ideal coincide.

i6 : R = ZZ/7[x,y,z]/(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

See also

Ways to use parameterTestIdeal :

For the programmer

The object parameterTestIdeal is a method function with options.