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 xyx^2 is represented as the LIST [x, y, x^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], [x, x], [x^2], [x^2], [x, x, x],
[x, x, x], [x, x^2], [x, x, x, x], [x,
x, x, x]];

[[[x, x, x], [x^2, x], [x, x, x], [x, x, x],
[x^2, x], [x, x, x], [x, x, x], [x, x, x],
[x, x^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]
])]
-------------------------------
```