ApCoCoA-1:NCo.IsFinite

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