ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 08 Aug 2018 03:31:56 -0500How can I compute the orbits of an automorphism group?http://ask.sagemath.org/question/43283/how-can-i-compute-the-orbits-of-an-automorphism-group/ I am new on automorphisms, need to know how to compute the orbits of an automorphism group in Sage.ASHWed, 08 Aug 2018 03:31:56 -0500http://ask.sagemath.org/question/43283/Number of graph automorphismshttp://ask.sagemath.org/question/43017/number-of-graph-automorphisms/ Using the below command in SAGE 8.2, the list of automorphisms for a graph could be attained.
G.automorphism_group().list()
What is the command for computing the number of graph automorphoisms?ASHSat, 14 Jul 2018 22:33:57 -0500http://ask.sagemath.org/question/43017/Automorphism group of weighted graphhttp://ask.sagemath.org/question/42762/automorphism-group-of-weighted-graph/I know we can use sage to find the group of automorphisms of a graph $G$:
G.automorphism_group().list()
However, the above way can only be used to the unweighted graph. So for example:
G = matrix([[0,10,0],
[10,0,1],
[0,1,0]])
G1 = Graph(G, weighted = True)
G1.show(edge_labels=True )
G.automorphism_group().list()
The result is:
[(), (0,2)]
However, this result is not correct (correct for unweighted case). This is because $AD\neq DA$, where
$$D = \begin{bmatrix} 0 & 0 & 1 \\\ 0 & 1 & 0 \\\ 1 & 0 & 0\end{bmatrix},$$ which is a permutation matrix and
$$A = \begin{bmatrix} 0 & 10 & 0 \\\ 10 & 0 & 1 \\\ 0 & 1 & 0\end{bmatrix},$$ which is an adjacency matrix.
Can we use SAGE to find the group of automorphisms of a graph?sleeve chenWed, 27 Jun 2018 20:22:14 -0500http://ask.sagemath.org/question/42762/Action of lattice automorphism group on discriminant grouphttp://ask.sagemath.org/question/40645/action-of-lattice-automorphism-group-on-discriminant-group/I have a lattice $L$ with automorphism group $G=Aut(L)$. The action of $G$ on $L$ should induce an action on the discriminant group $D={\tilde L}/L$ such that we have a group homomorphism $\phi: Aut(L) \rightarrow Aut(D)$. The kernel of this map will be a normal subgroup $N$ of $G$. I need to be able to compute the action of the quotient $G/N$ on $D$. In the actual example I am interested in $L$ has rank $20$ and is defined through its Gram Matrix. $L$ is an even lattice. A simpler model of this situation would be to take $L$ to be a root lattice, say the $A_2$ root lattice to be concrete, $Aut(L)$ is the dihedral group $D_6$ arising as the product of the $Z_2$ outer automorphism and the $S_3$ Weyl group of $A_2$. The dual lattice $\tilde L$ is the weight lattice of $A_2$ and the discriminant group ${\tilde L}/L$ is $Z_3$ with one non-trivial automorphism, taking $g \rightarrow g^{-1}$. In this simple case everything is computable by hand, but for the case I am interested in I only have $Aut(L)$ presented in terms of $20 \times 20$ matrix generators and computing by hand seems too difficult. Can anyone provide any hints on how to get sage to do this? I can compute $Aut(L)$ and $Aut(D)$ using sage, my problem is in figuring out how to determine $N$ and the action of the quotient $G/N$ on $D$.jahTue, 16 Jan 2018 14:37:35 -0600http://ask.sagemath.org/question/40645/