# ApCoCoA-1:NCo.LC

## NCo.LC

The leading coefficient of a polynomial in a free monoid ring.

### Syntax

NCo.LC(F:LIST):INT or RAT

### 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 NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before using this function. The default coefficient field is `Q`, and 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 monomials, which are LISTs 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 INT or RAT, which represents the leading coefficient of F with respect to the current word ordering. If

`F=0`, the function returns`0`.

#### Example

NCo.SetX(<quotes>abc</quotes>); F:=[[1,<quotes>ab</quotes>],[2,<quotes>aa</quotes>],[3,<quotes>bb</quotes>],[4,<quotes>bab</quotes>]]; NCo.SetOrdering(<quotes>ELIM</quotes>); NCo.LC(F); 2 ------------------------------- NCo.SetOrdering(<quotes>LLEX</quotes>); NCo.LC(F); 4 ------------------------------- NCo.LC([]); -- 0 polynomial 0 -------------------------------

### See also