Difference between revisions of "ApCoCoA-1:NC.AdMatrix"

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<title>NC.AdMatrix</title>
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<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.
 
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Please set non-commutative polynomial ring (via the command <ref>Use</ref>) before calling this function. For more information, please check the relevant commands and functions.
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Please set non-commutative polynomial ring (via the command <ref>ApCoCoA-1:Use|Use</ref>) before calling this function. For more information, please check the relevant commands and functions.
 
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<item>@param <em>M</em>: 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 <tt>x[2]y[1]x[2]^2</tt> is represented as the LIST [x[2], y[1], x[2]^2].</item>
 
<item>@param <em>M</em>: 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 <tt>x[2]y[1]x[2]^2</tt> is represented as the LIST [x[2], y[1], x[2]^2].</item>
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<seealso>
 
<seealso>
<see>NC.IsFinite</see>
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<see>ApCoCoA-1:NC.IsFinite|NC.IsFinite</see>
<see>Introduction to CoCoAServer</see>
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<see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see>
 
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Latest revision as of 10:12, 7 October 2020

This article is about a function from ApCoCoA-1.

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

NC.IsFinite

Introduction to CoCoAServer