# 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

```USE QQ[x[1..2],y[1..2]];
F1:= [[2x,y,x^2], [-9y,x^2,x^3]]; -- 2xyx^2-9yx^2x^3
F2:= [[2x,y,x^2], [y,x^3]]; -- 2xyx^2+yx^3
F3:= [[2x,y,x]]; -- 2xyx
NC.IsHomog(F1);
NC.IsHomog(F2);
NC.IsHomog(F3);
NC.IsHomog([F1,F2,F3]);
NC.IsHomog([F2,F3]);

False
-------------------------------
True
-------------------------------
True
-------------------------------
False
-------------------------------
True
-------------------------------
```