# Difference between revisions of "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 set non-commutative polynomial ring (via the command Use) before calling this function. For more information, please check the relevant commands and functions.

• @param F: a non-commutative polynomial or a LIST of non-commutative polynomials. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2xyx^2-9yx^2x^3+5 is represented as F:=[[2x,y,x^2], [-9y,x^2,x^3], ]. The zero polynomial 0 is represented as the empty LIST [].

• @return: a BOOL, which is True if F is homogeneous and False otherwise.

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