# ApCoCoA-1:NC.AdMatrix

## NC.AdMatrix

Construct an adjacency matrix of the Ufnarovski graph for a finite set of words in a non-commutative polynomial ring.

### Syntax

NC.AdMatrix(M:LIST):LIST

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

Please set non-commutative polynomial ring (via the command Use) before calling this function. For more information, please check the relevant commands and functions.

@param

*M*: a LIST of words (or terms) in the defining ring. Note that each word is represented as a LIST, and that each element in the LIST involves only one indeterminate or none (a constant). For instance, the word`x[2]y[1]x[2]^2`is represented as the LIST [x[2], y[1], x[2]^2].@return: a LIST consisting of two elements. The first element in the LIST is a LIST of words that are the vertices in the Ufnarovski graph of M, and the second element is an adjacency matrix of the Ufnarovski graph.

#### Example

Use ZZ/(2)[x[1..3]]; M:=[[x[3]^3], [x[1], x[2]], [x[2]^2], [x[1]^2], [x[2], x[3], x[1]], [x[1], x[3], x[1]], [x[1], x[3]^2], [x[2], x[3], x[2], x[3]], [x[1], x[3], x[2], x[3]]]; NC.AdMatrix(M); [[[x[3], x[2], x[1]], [x[3]^2, x[1]], [x[1], x[3], x[2]], [x[2], x[3], x[2]], [x[3]^2, x[2]], [x[2], x[1], x[3]], [x[3], x[1], x[3]], [x[3], x[2], x[3]], [x[2], x[3]^2]], Mat([ [0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 0, 1], [0, 1, 0, 0, 1, 0, 0, 0, 0] ])] -------------------------------

### See also