# ApCoCoA-1:NC.IsGB

## NC.IsGB

Check if a list of polynomials is a Groebner basis.

### Syntax

NC.IsGB(Polynomials: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.

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

@param

*Polynomials*: a LIST of polynomials in`K<X>`. Each polynomial in`K<X>`is represented as a LIST of LISTs, which are pairs of form [c, w] where c is in`K`and w is a word in`X*`. Unit in`X*`is empty word represented as an empty STRING "".`0`polynomial is represented as an empty LIST []. For example, polynomial`F:=xy-y+1`in`K<x,y>`is represented as`F:=[[1,"xy"], [-1, "y"], [1,""]]`.@return: a BOOL which is True if

`Polynomials`is a GB 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>]]; Polynomials := [F1, F2,F3,F4]; NC.IsGB(Polynomials); -- LLEX ordering (default ordering) False ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.IsGB(Polynomials); False -------------------------------

### See also