2015-04-20 23:35:16 +0200 | answered a question | Add generator to a group? Combine generators of two groups? Thank you Vincent, that's what I am looking for. I did the test to compare the speed, I did it first for small groups repeat 5000 times, then for large groups. Notes: Here is the python/sage code: |

2015-04-20 01:28:16 +0200 | received badge | ● Scholar (source) |

2015-04-18 22:50:47 +0200 | asked a question | Add generator to a group? Combine generators of two groups? Hi guys, I am wondering how to efficiently do the following two things in Sage add a generator h to a existing group G to create a new group, e.g. from `sage: h = (3,4) sage: G = PermutationGroup([(1,2),(1,3)])` how to get a new group N with generators [(1,2),(1,3),(3,4)]. I can do this by using `G.gens()` and adding`(3,4)` to the list and calling`PermutationGroup()` , but it looks awkward, is there a more efficient way?create a new group from generators of two existing group, e.g. from `sage: G = PermutationGroup([(1,2),(1,3)]) sage: H = PermutationGroup([(3,4)])` how to get a new group N with generators [(1,2),(1,3),(3,4)]? Currently I can do this by : `N = PermutationGroup(G.gens()+H.gens())`
Thanks, Kevin |

2015-03-11 12:05:45 +0200 | received badge | ● Student (source) |

2015-03-10 20:20:58 +0200 | answered a question | checking isomorphism for weighted bipartite graph Thank you for your help, I wasn't able to find the documentation for is_isomorphic yesterday, now I finally got it. In fact, I don't even need to do the edge labeling, when I do WW = BipartiteGraph(Z,weighted=True), the numbers in the matrix are treated as weights, so I can get the result I want by just doing WW.is_isomorphic(XX,edge_labels=True). In fact, I am interested in a more general isomorphism test. For example, in X = Matrix([(1,1,2,2),(1,1,2,3),(1,2,2,1)]), I not only want to be able to treat swapping rows and columns as equivalent (which equivalent to change the labeling of nodes on the left and right of the biparitite graph separately), I can also do bijections on each rows. So for row one of X, (1,1,2,2) can be replaced with (2,2,1,1), for row two of X, (1,1,2,3) can be replaced with (1,1,3,2) (2,2,3,1) (2,2,1,3) (3,3,1,2) (3,3,2,1). I am wondering if there exist algorithms to do that directly? Right now the only way I can think of is to first list all combinations of bijections, in this example. there are 2 * 6 * 2 = 24 equivalent cases, then for each of them, I do a isomorphism test with the original matrix, if at least one graph out of 24 is isomorphism with the original graph, I consider them equivalent. However, this approach will become intractable even the size of the matrix is not that big. |

2015-03-10 07:14:29 +0200 | received badge | ● Editor (source) |

2015-03-10 07:13:07 +0200 | asked a question | checking isomorphism for weighted bipartite graph Hi, guys, I am working on a problem involving checking if two weighted bipartite graphs are isomorphic. I saw I can define a weighted graph in sage like this: I swapped rows and columns of matrix defining X to get Y, so Y is isomorphic to X, But since my graphs are weighted, I changed one element in Y from 1 to 2 to get W, yet it still tell me XX and WW are isomorphic Are there other functions I can use to check isomorphism for weighted bipartite graph? |

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.