# ApCoCoA-1:NCo.AdMatrix

## NCo.AdMatrix

Construct an adjacency matrix of the Ufnarovski graph for a finite set of words.

### Syntax

NCo.AdMatrix(X:STRING, 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.

@param

*X*: alphabet (or set of indeterminates) generating the free monoid`K<X>`. It is of STRING type.@param

*M*: a LIST of words (or terms) in`<X>`which generates the monoid ideal`<M>`. Each word is represented as a STRING. For example,`xy^2x`is represented as "xyyx", and the identity is represented as the empty string "".@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

X:="xy"; M:=["xxx","yxy","xyx"]; NCo.AdMatrix(X, M); [["xx", "xy", "yx", "yy"], Mat([ [0, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 1, 1] ])] ------------------------------- X:="xy"; M:=["xxx","yxy","xyx","yyx","yyy"]; NCo.AdMatrix(X, M); [["xx", "xy", "yx", "yy"], Mat([ [0, 1, 0, 0], [0, 0, 0, 1], [1, 0, 0, 0], [0, 0, 0, 0] ])] -------------------------------

### See also