# ApCoCoA-1:NC.LW

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## NC.LW

The leading word (or term) of a non-zero polynomial in a non-commutative polynomial ring.

### Syntax

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

### 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=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 LIST, which is the leading word of F with respect to the current word ordering.

#### Example

```USE QQ[x[1..2]];
F:= [[x^2], [2x,x], [3x,x],[4x^2]]; -- x^2+2xx+3xx+4x^2
NC.SetOrdering("LLEX");
NC.LW(F);

[x^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("LRLEX");
NC.LW(F);

[x^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("ELIM");
NC.LW(F);

[x^2]
-------------------------------
-- Done.
-------------------------------
NC.SetOrdering("DEGRLEX");
NC.LT(F);

[x^2]
-------------------------------
```