ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 28 Nov 2012 01:49:45 -0600Dual Cells and Face Posethttps://ask.sagemath.org/question/9578/dual-cells-and-face-poset/Hello.
I would like to create a procedure in Sage to find the dual cell of a simplex $\sigma$ in a simplicial complex $K$. The dual cell $D(\sigma, K)$ of $\sigma$ is a subcomplex of the first barycentric subdivision of $K$. The vertex set is given by the barycentres of all cofaces of $\sigma$, and the simplices are joins of barycentres of the form $\widehat{\sigma_0} \widehat{\sigma_1} ... \widehat{\sigma_s}$ with $\sigma \leq \sigma_0 \leq ... \leq \sigma_s$.
My plan of attack is to view K as a poset, then find the maximal increasing chains $[\sigma_0,..., \sigma_s]$ in K which satisfy $\sigma_0 = \sigma$ . These chains would then be the maximal faces of the dual cell $D(\sigma, K)$.
Creating the poset and finding the maximal chains of simplices is fine. However, if I have a maximal chain $[\sigma_0,..., \sigma_s]$ a problem occurs when checking if $\sigma_0 = \sigma$ - Sage sees $\sigma_0$ as just an element of the poset and not as simplex and $\sigma$ as a simplex but not an element of the poset so the equality is never satisfied.
How can I correct this?
Thanks,
Chris .DG44Wed, 28 Nov 2012 01:49:45 -0600https://ask.sagemath.org/question/9578/