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

## NC.LW

Leading word of a non-zero polynomial in a non-commutative polynomial ring.

### Syntax

```NC.LW(F:LIST):STRING
```

### Description

Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.

Please set non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

• @param F: a non-zero 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: a LIST, which is the leading word of F with respect to the current word ordering.

#### Example

```NC.SetX(<quotes>abc</quotes>);
F:=[[1,<quotes>ab</quotes>],[1,<quotes>aa</quotes>],[1,<quotes>bb</quotes>],[1,<quotes>bab</quotes>]];
NC.LW(F); -- LLEX ordering (default ordering)
bab
-------------------------------
NC.SetOrdering(<quotes>ELIM</quotes>);
NC.LW(F);
aa
-------------------------------
NC.LW([]);
```