Difference between revisions of "ApCoCoA-1:NCo.IsFinite"

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<item>@param <em>X</em>: alphabet (or set of indeterminates) generating the free associative <tt>K</tt>-algebra <tt>K&lt;X&gt;</tt>. It is of STRING type.</item>
 
<item>@param <em>X</em>: alphabet (or set of indeterminates) generating the free associative <tt>K</tt>-algebra <tt>K&lt;X&gt;</tt>. It is of STRING type.</item>
<item>@param <em>M</em>: a LIST of words (or terms) in <tt>K&lt;X&gt;</tt> which generates the monoid ideal <tt>&lt;M&gt;</tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as <quotes>xyyx</quotes>, and the identity is represented as the empty string <quotes></quotes>.</item>
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<item>@param <em>M</em>: a LIST of words (or terms) in <tt>K&lt;X&gt;</tt> which generates the monoid ideal <tt>&lt;M&gt;</tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as "xyyx", and the identity is represented as the empty string "".</item>
 
<item>@return: a BOOL value which is True if <tt>K</tt>-vector space <tt>K&lt;X&gt;/&lt;M&gt;</tt> is finite and False otherwise.</item>
 
<item>@return: a BOOL value which is True if <tt>K</tt>-vector space <tt>K&lt;X&gt;/&lt;M&gt;</tt> is finite and False otherwise.</item>
 
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<see>NCo.AdMatrix</see>
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<see>ApCoCoA-1:NCo.AdMatrix|NCo.AdMatrix</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 13:40, 29 October 2020

This article is about a function from ApCoCoA-1.

NCo.IsFinite

Check whether the K-dimension dim(K<X>/<M>) is finite, where <M> is an monoid ideal generated by a finite set M of words.

Syntax

NCo.IsFinite(X:STRING, M:LIST):BOOL

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 associative K-algebra K<X>. It is of STRING type.

  • @param M: a LIST of words (or terms) in K<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 BOOL value which is True if K-vector space K<X>/<M> is finite and False otherwise.

Example

X:="xy";
M:=["xxx","yxy","xyx"];
NCo.IsFinite(X, M);

False
-------------------------------
X:="xy";
M:=["xxx","yxy","xyx","yyx","yyy"];
NCo.IsFinite(X, M);

True
-------------------------------

See also

NCo.AdMatrix

Introduction to CoCoAServer