What's the easiest way to calculate a Hironaka standard basis using SageMath?

asked 2020-12-01 18:44:06 -0600

joshuarbholden gravatar image

Hi, everyone!

I'm trying to do some computations with (truncated) multivariable power series, which I'd like to put into Hironaka standard basis form. This is almost the same as a Groebner basis, except that the "leading" terms have smallest degree instead of largest. This requires slight changes to the algorithms in order to make sure they terminate. Does anyone know if this has been implemented in Sage or have a good way to fake it? I don't use Sage a lot and I can't find anything obvious in the documentation so I thought I'd ask before trying to re-implement something.

Thanks very much!

----Josh

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Comments

Is this related to local orderings as defined in Singular?

rburing gravatar imagerburing ( 2020-12-02 07:38:18 -0600 )edit

Yes and no. Changing the monomial ordering is necessary but not sufficient (AFAICT) to calculate Hironaka standard bases.

joshuarbholden gravatar imagejoshuarbholden ( 2020-12-02 21:31:32 -0600 )edit

You might have more luck asking on the sage-support mailing list.

rburing gravatar imagerburing ( 2020-12-04 05:53:23 -0600 )edit

Will do, thanks!

joshuarbholden gravatar imagejoshuarbholden ( 2020-12-12 13:36:14 -0600 )edit