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TestIdeals :: canonicalIdeal

canonicalIdeal -- given a ring, produces an ideal isomorphic to the canonical module

Synopsis

Description

Given a ring R, typically a domain, this produces an ideal isomorphic to the canonical module of R. This will not always produce the same ideal, especially in a non-domain. It uses the function embedAsIdeal from Divisor.m2.

i1 : S = QQ[x,y,u,v];
i2 : T = QQ[a,b];
i3 : f = map(T, S, {a^3, a^2*b, a*b^2, b^3});

o3 : RingMap T <--- S
i4 : R = S/(ker f);
i5 : canonicalIdeal(R)

o5 = ideal (v, u)

o5 : Ideal of R

Here’s an example in a non-domain.

i6 : R = ZZ/13[x,y,z]/ideal(x*y, x*z, y*z);
i7 : canonicalIdeal(R)

o7 = ideal (y - 5z, x + 4z)

o7 : Ideal of R

Ways to use canonicalIdeal :