@antoinechambertloir@mathstodon.xyz
Post #1368980
2026-03-23 15:31 UTC
@jdw that would be true for all of the specific monomial orderings I know of, but I'm not sure about the general case.
Replies (1)
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@jdw@mathstodon.xyz 2026-03-23 16:51
@antoinechambertloir Yes, all the standard examples of monomial orders are *weight orders* for some concrete rational weight vectors. For these it is easy to see that they are well-founded. (I'm not 100% sure everything works fine with non-rational weights because of the constructive difficulties with real numbers.) Appearantly https://link.springer.com/chapter/10.1007/3-540-15984-3_321 contains a proof that every ordering is a weight ordering, but unfortunately I can't access the paper. I doubt the proof will be constructive.