Zulip Chat Archive

Stream: maths

Topic: polynomial ring homs


view this post on Zulip Johan Commelin (Sep 01 2020 at 17:16):

@Scott Morrison you mentioned on a PR page that there are good reasons to not bundle up all the mv_polynomial.{eval,map,rename,*} into ring homs directly. Can you please tell me what those reasons are?

view this post on Zulip Scott Morrison (Sep 01 2020 at 22:04):

The problem is just that for some of these to even be ring homs requires commutativity assumptions (typically on the "target"), yet we sometimes want to use the maps when the targets are not commutative.

view this post on Zulip Scott Morrison (Sep 01 2020 at 22:05):

A concrete example is that to prove Cayley-Hamilton we use the evaluation map for polynomials with matrix coefficients, which is not a ring hom.

view this post on Zulip Scott Morrison (Sep 01 2020 at 22:06):

We could just have two names, e.g. eval_noncomm (which might be a bundled add_monoid_hom) and eval (as a ring hom).

view this post on Zulip Johan Commelin (Sep 02 2020 at 03:38):

Ok, that makes total sense. Thanks.


Last updated: May 14 2021 at 19:21 UTC