I have an ideal in the polynomial ring F2[x,y,z] given by I=(1+x+y+xy;1+y+z+yz;1+x+z+xz). The annihilator of this ideal is generated by
fxy=∑n,m∈Zxnym, fxz=∑n,m∈Zxnzm, fzy=∑n,m∈Zznym
because for example fxyI=((1+1+1+1)fxy,(1+1+z+z)fxy,(1+1+z+z)fxy)=(0,0,0).
Can I show this in sage? More generally, given an ideal like the above in F2[x,y,z] can I find the generators of its annihilator?