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.Thu, 03 Jul 2014 00:25:08 +0200Categorical product of simplicial complexeshttps://ask.sagemath.org/question/23170/categorical-product-of-simplicial-complexes/Does Sage have some function that takes the *categorical* product of two finite simplicial complexes? I see that the SimplicialComplex library has a product() function that appears to take the *topological* product of two complexes (details here: http://www.sagemath.org/doc/reference/homology/sage/homology/simplicial_complex.html), but this isn't what I'm looking for.
The example given on the linked webpage is Simplex(1).product(Simplex(1)), which returns [('L0R0', 'L0R1', 'L1R1'), ('L0R0', 'L1R0', 'L1R1')], or a square with a diagonal through it. This is what I would expect from a topological product, since the product of two lines is a square. However, the *categorical* product of two complexes is different and is in general not homeomorphic to their topological product. The categorical product of two edges (1-simplexes) should be a tetrahedron and not a square.
Is there a Sage function that will do this for me? I'm not familiar with the markdown syntax on this forum so sorry about the poor formatting.Vikram SaraphThu, 03 Jul 2014 00:25:08 +0200https://ask.sagemath.org/question/23170/