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

From ApCoCoAWiki

(New page: <command> <title>NCo.IsFinite</title> <short_description> Check whether the <tt>K</tt>-dimension <tt>dim(K<X>/<M>)</tt> is finite, where <tt><M></tt> is an monoid ideal g...) |
|||

Line 20: | Line 20: | ||

NCo.IsFinite(X, M); | NCo.IsFinite(X, M); | ||

− | + | False | |

------------------------------- | ------------------------------- | ||

X:="xy"; | X:="xy"; | ||

Line 26: | Line 26: | ||

NCo.IsFinite(X, M); | NCo.IsFinite(X, M); | ||

− | + | True | |

------------------------------- | ------------------------------- | ||

</example> | </example> |

## Revision as of 19:18, 6 June 2013

## 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