ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 14 Jul 2017 22:52:42 +0200Compute preimage of Idealshttps://ask.sagemath.org/question/38264/compute-preimage-of-ideals/It's me again. I am wondering how to compute the preimage of an ideal $J\subseteq B$ in a ring along a ring homomorphism $f\colon A\to B$. 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.Fri, 14 Jul 2017 19:27:34 +0200https://ask.sagemath.org/question/38264/compute-preimage-of-ideals/Comment by vdelecroix for <p>It's me again. I am wondering how to compute the preimage of an ideal $J\subseteq B$ in a ring along a ring homomorphism $f\colon A\to B$. 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>
<p>P.S.: The question of how to compute kernels of homorphisms of affine algebras over a field is of course equivalent.</p>
https://ask.sagemath.org/question/38264/compute-preimage-of-ideals/?comment=38267#post-id-38267It would be better if you start with concrete examples of `A`, `B` and `f` (ie Sage code to generate them).Fri, 14 Jul 2017 22:52:42 +0200https://ask.sagemath.org/question/38264/compute-preimage-of-ideals/?comment=38267#post-id-38267