Den onsdag den 12. august 2015 kl. 15.26.09 UTC+2 skrev mmarco: > > The TL representation involves the product of a nuumber of matrices that > is linear on the number of crossings, and the complexity of such a matrix > is also polynomial on the number of strands (around fourth power maybe?). >
In the code in #19011, the representation for n strands is actually a direct sum of roughly n/2 representations. I'm not sure what you mean exactly by the 'complexity' of the matrix representations but the sums of the squares of the dimensions of the relevant spaces are exactly the Catalan numbers which grow asymptotically like something like 4^n / n^(3/2). It just occurred to me though, that the problematic cases could probably become a lot less problematic by imposing sparsity. That should probably be the default assumption: sage: benchmark() Test 1: A very long braid with very few strands Braid: (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 , 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1) Braid rep: 0.06 seconds, Kauffman bracket: 9.99 seconds Test 2: A very simple braid on quite a few strands Braid: (1, 2, 3, 4, 5, 6, 7, 8) Braid rep: 0.04 seconds, Kauffman bracket: 0.00 seconds - Søren -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
