Difference between revisions of "ApCoCoA-1:NC.AdMatrix"
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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. | ||
<par/> | <par/> | ||
| − | 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. | + | 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. |
<itemize> | <itemize> | ||
<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> | + | <see>ApCoCoA-1:NC.IsFinite|NC.IsFinite</see> |
| − | <see>Introduction to CoCoAServer</see> | + | <see>ApCoCoA-1:Introduction to CoCoAServer|Introduction to CoCoAServer</see> |
</seealso> | </seealso> | ||
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<key>AdMatrix</key> | <key>AdMatrix</key> | ||
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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
