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.Sat, 12 Dec 2020 20:36:14 +0100What's the easiest way to calculate a Hironaka standard basis using SageMath?https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/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
Wed, 02 Dec 2020 01:44:06 +0100https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/Comment by joshuarbholden for <p>Hi, everyone!</p>
<p>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.</p>
<p>Thanks very much!</p>
<p>----Josh</p>
https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54663#post-id-54663Will do, thanks!Sat, 12 Dec 2020 20:36:14 +0100https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54663#post-id-54663Comment by joshuarbholden for <p>Hi, everyone!</p>
<p>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.</p>
<p>Thanks very much!</p>
<p>----Josh</p>
https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54531#post-id-54531Yes and no. Changing the monomial ordering is necessary but not sufficient (AFAICT) to calculate Hironaka standard bases.Thu, 03 Dec 2020 04:31:32 +0100https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54531#post-id-54531Comment by rburing for <p>Hi, everyone!</p>
<p>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.</p>
<p>Thanks very much!</p>
<p>----Josh</p>
https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54514#post-id-54514Is this related to [local orderings](https://www.singular.uni-kl.de/Manual/latest/sing_963.htm) as defined in Singular?Wed, 02 Dec 2020 14:38:18 +0100https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54514#post-id-54514Comment by rburing for <p>Hi, everyone!</p>
<p>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.</p>
<p>Thanks very much!</p>
<p>----Josh</p>
https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54550#post-id-54550You might have more luck asking on the sage-support mailing list.Fri, 04 Dec 2020 12:53:23 +0100https://ask.sagemath.org/question/54506/whats-the-easiest-way-to-calculate-a-hironaka-standard-basis-using-sagemath/?comment=54550#post-id-54550