# Difference between revisions of "ApCoCoA-1:NC.Deg"

## NC.Deg

The (standard) degree of a polynomial in a non-commutative polynomial ring.

### Syntax

```NC.Deg(F:LIST):INT
```

### 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. 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: an INT which represents the standard degree of F. Note that the standard degree of 0 is 0.

#### Example

```NC.SetX(<quotes>abc</quotes>);
F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]];
NC.Deg(F);
3
-------------------------------
NC.Deg([]); -- 0 polynomial
0
-------------------------------
```