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

## 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
-------------------------------
```