# ApCoCoA-1:NCo.IsFinite

From ApCoCoAWiki

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

### See also