# 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 -------------------------------

### See also