# ApCoCoA-1:NC.LW

## NC.LW

Leading word of a polynomial in a free monoid 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 ring environment *coefficient field* `K`, *alphabet* (or set of indeterminates) `X` and *ordering* via the functions NC.SetFp, NC.SetX and NC.SetOrdering, respectively, before calling the function. The default coefficient field is `Q`. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F*: a polynomial in`K<X>`. Each polynomial is represented as a LIST of LISTs, which are pairs of form [C, W] where C is a coefficient and W is a word (or term). Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in`<X>`and C is the coefficient of W. For example, the polynomial`F=xy-y+1`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial`0`is represented as the empty LIST [].@return: a STRING which represents the leading term of F w.r.t. the current ordering. If

`F=0`, the function returns nothing.

#### 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