# ApCoCoA-1:NC.LW

## 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=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

USE QQ[x[1..2]]; F:= [[x[1]^2], [2x[1],x[2]], [3x[2],x[1]],[4x[2]^2]]; -- x[1]^2+2x[1]x[2]+3x[2]x[1]+4x[2]^2 NC.SetOrdering(<quotes>LLEX</quotes>); NC.LW(F); [x[1]^2] ------------------------------- -- Done. ------------------------------- NC.SetOrdering(<quotes>LRLEX</quotes>); NC.LW(F); [x[2]^2] ------------------------------- -- Done. ------------------------------- NC.SetOrdering(<quotes>ELIM</quotes>); NC.LW(F); [x[1]^2] ------------------------------- -- Done. ------------------------------- NC.SetOrdering(<quotes>DEGRLEX</quotes>); NC.LT(F); [x[1]^2] -------------------------------

### See also