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, 30 Apr 2022 09:16:08 +0200How to find the dimension of Grobner basishttps://ask.sagemath.org/question/62225/how-to-find-the-dimension-of-grobner-basis/I have a set POLY of multivariate polynomials over integer. From this set, we can calculate Grobner basis as follows:
I=(POLY)*RING
I=Ideal(I)
B = I.groebner_basis()
where RING is the corresponding polynomial ring. I want to find the dimension of B as defined in https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#:~:text=The%20dimension%20is%20the%20maximal,is%20a%20power%20of%20x.
How to find that in Sage?Sat, 30 Apr 2022 09:09:45 +0200https://ask.sagemath.org/question/62225/how-to-find-the-dimension-of-grobner-basis/Answer by tmonteil for <p>I have a set POLY of multivariate polynomials over integer. From this set, we can calculate Grobner basis as follows:</p>
<pre><code>I=(POLY)*RING
I=Ideal(I)
B = I.groebner_basis()
</code></pre>
<p>where RING is the corresponding polynomial ring. I want to find the dimension of B as defined in <a href="https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis#:~:text=The%20dimension%20is%20the%20maximal,is%20a%20power%20of%20x">https://en.wikipedia.org/wiki/Gr%C3%B...</a>.</p>
<p>How to find that in Sage?</p>
https://ask.sagemath.org/question/62225/how-to-find-the-dimension-of-grobner-basis/?answer=62226#post-id-62226You link is refering to the dimension of the ideal, so you can just use:
sage: I.dimension()Sat, 30 Apr 2022 09:16:08 +0200https://ask.sagemath.org/question/62225/how-to-find-the-dimension-of-grobner-basis/?answer=62226#post-id-62226