ApCoCoA-1:NCo.AdMatrix

This article is about a function from ApCoCoA-1.

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

NCo.IsFinite

Introduction to CoCoAServer