# Difference between revisions of "ApCoCoA-1:NC.IsGB"

Line 63: | Line 63: | ||

<type>apcocoaserver</type> | <type>apcocoaserver</type> | ||

<type>groebner</type> | <type>groebner</type> | ||

+ | <type>ideal</type> | ||

+ | <type>non_commutative</type> | ||

</types> | </types> | ||

<key>gbmr.IsGB</key> | <key>gbmr.IsGB</key> |

## Revision as of 14:54, 14 December 2010

## NC.IsGB

Checks whether a list of polynomials over a free associative `K`-algebra is a Groebner basis of the ideal generated by polynomials.

### Syntax

NC.IsGB(G: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.

Please set ring environment coefficient field `K`, alphabet (or indeterminates) `X` and ordering through the functions NC.SetFp(Prime), NC.SetX(X) and NC.SetOrdering(Ordering), respectively, before calling the function. Default coefficient field is `Q`. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*G*: a LIST of polynomials in`K<X>`. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each term is represented as a STRING. For example,`xy^2x`is represented as "xyyx", unit is represented as an empty string "". Then, polynomial`F=xy-y+1`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].`0`polynomial is represented as an empty LIST [].@return: a BOOL value which is True if G is a Groebner basis and False otherwise.

#### Example

NC.SetX(<quotes>xyt</quotes>); F1 := [[1,<quotes>xx</quotes>], [-1,<quotes>yx</quotes>]]; F2 := [[1,<quotes>xy</quotes>], [-1,<quotes>ty</quotes>]]; F3 := [[1,<quotes>xt</quotes>], [-1, <quotes>tx</quotes>]]; F4 := [[1,<quotes>yt</quotes>], [-1, <quotes>ty</quotes>]]; G := [F1, F2,F3,F4]; NC.IsGB(G); -- LLEX ordering (default ordering) False ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.IsGB(G); False -------------------------------

### See also