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.Sun, 03 Mar 2013 08:59:48 +0100nilpotent adjacency matrixhttps://ask.sagemath.org/question/9870/nilpotent-adjacency-matrix/i wish to define a nilpotent adjacency matrix.
example vertex adjacency matrix of a graph ($K_4$ minus an edge) is
A=
[0 1 1 0]
[1 0 1 1]
[1 1 0 1]
[0 1 1 0]
where N=4 vertices
so for all entries $A_{ij}$ i wish to define a function to replace the 1's by $b_j$
so for the example above i get a nilpotent matrix
B=
[0 $b_2$ $b_3$ 0]
[$b_1$ 0 $b_3$ $b_4$]
[$b_1$ $b_2$ 0 1]
[0 $b_2$ $b_3$ 0]
where the $b_j$ where $i,j\in${1,2,3,4} obey the following rules of multiplication:
$b_jb_i=b_ib_j$ and $b_j^2=0$ (so i also need to define a function for these rules)
so for the nilpotent adjacency matrix i can define matrix multiplication using the above rules for its entries i.e. $B^N$
i'd like the function to be something like nil(B,k)
and for it to print the trace of $B^k$
e.g. $nil(B,2)=2b_1b_2+2b_1b_3+2b_2b_3+2b_2b_4+2b_3b_4$
i'll try to work on this myself too in the meantime, but this is probably the most complicated function i've had to do.. mainly due to redefining the adjacency matrixjtaaSun, 03 Mar 2013 08:59:48 +0100https://ask.sagemath.org/question/9870/