On Wed, 16 Oct 2024 at 16:45, Nils Bruin <nbr...@sfu.ca> wrote: > > On Wednesday 16 October 2024 at 06:43:30 UTC-7 Georgi Guninski wrote: > > sage: Kx.<x,y>=QQ[] > sage: I=Ideal([x*y]) > sage: gb=I.groebner_basis(algorithm='singular:stdfglm') > > TypeError: Singular error: > ? The ideal i has to be 0-dimensional > > I believe computing the dimension of ideal requires computing groebner basis > and even if this a false, computing the dimension of ideal will detect > the constant ideal. If computing the dimension of ideal is efficient, > this will be a major achievement. > > So `stdfglm` recognizes the ideal is not 0 dimensional, something else > did the heavy computation of the dimension, so `stdfglm` is slower than > the `else`. > > Is the above reasoning correct? > > No it is not. The error above only indicates that the algorithm found a > contradiction to the assumption that the ideal is 0-dimensional; not that it > computed what the dimension actually is. > > groebner bases of 0-dimensional ideals have been proven to be easier to > compute than the general case (there are better complexity bounds for them), > so it is quite conceivable to that there is something to gain by writing an > algorithm that proceeds on the assumption the ideal is 0-dimensional and > bails as soon as it finds something that is inconsistent with that > assumption. I'd assume the singular documentation would have a reference to a > relevant paper discussing the strategy followed by stdfglm
The Singular documentation is here and it doesn't have any reference: https://www.singular.uni-kl.de/Manual/4-0-3/sing_403.htm The FGLM algorithm is for converting a zero-dimensional Groebner basis for one monomial ordering to a basis for another ordering. It sounds like stdfglm works in three steps: 1. Compute basis in degrevlex ordering. 2. Check the basis is zero dimensional. 3. Use FGLM to convert to lex ordering. In this case the basis is not zero dimensional so the FGLM step is not attempted (even though the basis conversion is trivial). -- Oscar -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/CAHVvXxTOoYr%3DTaUoYW%3Dfvp%3DKCeH4uHRzoNOksa22GOH%2BrktcGw%40mail.gmail.com.
