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<X></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<X></tt>. It is of STRING type.</item> | ||
| − | <item>@param <em>M</em>: a LIST of words (or terms) in <tt>K<X></tt> which generates the monoid ideal <tt><M></tt>. Each word is represented as a STRING. For example, <tt>xy^2x</tt> is represented as | + | <item>@param <em>M</em>: a LIST of words (or terms) in <tt>K<X></tt> which generates the monoid ideal <tt><M></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<X>/<M></tt> is finite and False otherwise.</item> | <item>@return: a BOOL value which is True if <tt>K</tt>-vector space <tt>K<X>/<M></tt> is finite and False otherwise.</item> | ||
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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
