# Singular

 Page 1 of 1 [ 2 posts ]
 Print view | E-mail friend Previous topic | Next topic
Author Message
 Post subject: Gröbner basis on Sullivan minimal modelsPosted: Tue Oct 02, 2012 10:43 pm

Joined: Tue Oct 02, 2012 9:53 pm
Posts: 1
We consider a Sullivan minimal model, in the particular case we take an pure Sullivan minimal model, we would like to construct a Gröbner basis in this algebra, note that $d(\Lambda Q\otimes P)=\Lambda Q.d(P)$ is the ideal in the polynomial algebra $\Lambda Q$ generated by $d(P)$. We know that the Gröbner basis is easily computable in many cases, we can determine if two ideals are equal by looking at their reduced Gröbner bases. It is well known that the differential $d$ of any element of $V$ is a polynomial in $\Lambda V$ with no linear term, wich in particular means that there is a homogeneous basis ${v_i}_i\geq 1$ of $V$ for wich $dv_i\in \Lambda V_<i$, where $V_<i$ denotes the subspace of $W$ generated by \${v_i}_j<i, we want to construct by the same manner the Gröbner basis in the Sullivan minimal model as graded algebra, in particular by using the Buchberger’s Criterion, we can then give a set of polynomials with odd degree, by rational dichotomy.

Top

 Post subject: Re: Gröbner basis on Sullivan minimal modelsPosted: Wed Oct 03, 2012 8:26 pm

Joined: Tue Jun 23, 2009 10:33 pm
Posts: 51
Location: Kaiserslautern
Hi, and welcome to our forum!

Yes, Singular works with super-commutative algebras (http://www.singular.uni-kl.de/Manual/3- ... htm#SEC566) and their quotients if this is what you are asking about.

Cheers,
Oleksandr

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 You can post new topics in this forumYou can reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

 It is currently Thu Feb 21, 2019 11:41 pm