annihilator of a module

The annihilator of a module M over a ring R, ann(M) = { f in R | fM = 0 }, is computed using the annihilator function.

i1 : R = QQ[a..i];

i2 : M = cokernel genericMatrix(R,a,3,3)

o2 = cokernel | a d g |
              | b e h |
              | c f i |

                            3
o2 : R-module, quotient of R

i3 : annihilator M

o3 = ideal(c*e*g - b*f*g - c*d*h + a*f*h + b*d*i - a*e*i)

o3 : Ideal of R

You may also use the abbreviation annihilator

i4 : ann (M/(a*M))

o4 = ideal (a, c*e*g - b*f*g - c*d*h + b*d*i)

o4 : Ideal of R