# ApCoCoA-1:NC.IsHomog

## NC.IsHomog

Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial ring.

### Syntax

```NC.IsHomog(F: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 set of indeterminates) X and ordering via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

• @param F: a polynomial or a LIST of polynomials in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].

• @return: a BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.

#### Example

```NC.SetX(<quotes>xy</quotes>);
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]];
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]];
F := [F1,F2];
NC.IsHomog(F);
False
-------------------------------
NC.IsHomog(F1);
True
-------------------------------
NC.IsHomog(F2);
False
-------------------------------
```