# 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=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5 is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. 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[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3]]; -- 2x[1]y[1]x[2]^2-9y[2]x[1]^2x[2]^3
F2:= [[2x[1],y[1],x[2]^2], [y[2],x[2]^3]]; -- 2x[1]y[1]x[2]^2+y[2]x[2]^3
F3:= [[2x[1],y[1],x[2]]]; -- 2x[1]y[1]x[2]
NC.IsHomog(F1);
NC.IsHomog(F2);
NC.IsHomog(F3);
NC.IsHomog([F1,F2,F3]);
NC.IsHomog([F2,F3]);

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