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Compute preimage of Ideals

It's me again. I am wondering how to compute the preimage of an ideal JB in a ring along a ring homomorphism f:AB. For simplicity I would be fine with assuming A and B are polynomial rings of finitely many variables over a field. As far as I know, preimages can then be computed algorithmically using Gröbner bases so I think this should be implemented in Sage. However I did not find such a possibility when browsing through the documentation. I hope you can help me (and maybe also point me to where such issues are documented). Thank you!

Compute preimage of Ideals

It's me again. I am wondering how to compute the preimage of an ideal JB in a ring along a ring homomorphism f:AB. For simplicity I would be fine with assuming A and B are polynomial rings of finitely many variables over a field. As far as I know, preimages can then be computed algorithmically using Gröbner bases so I think this should be implemented in Sage. However I did not find such a possibility when browsing through the documentation. I hope you can help me (and maybe also point me to where such issues are documented). Thank you!

P.S.: The question of how to compute kernels of homorphisms of affine algebras over a field is of course equivalent.