# 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):STRING NC.LT(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([]);

### See also