# ApCoCoA-1:NC.LC

## NC.LC

Leading coefficient of a polynomial over a free associative K-algebra.

### Syntax

NC.LC(F:LIST):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.

Before calling the function, please set ring environment coefficient field `K`, alphabet `X` and ordering through the functions NC.SetFp(Prime) (or NC.UnsetFp()), NC.SetX(X) and NC.SetOrdering(Ordering) respectively. Default coefficient field is `Q`. Default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F*: a polynomial in`K<X>`. Each polynomial in`K<X>`is represented as a LIST of LISTs, which are pairs of form`[c, w]`where c is in`K`and w is a word in`X*`. Unit in`X*`is empty word represented as an empty string "".`0`polynomial is represented as an empty list. For example, polynomial`F:=xy-y+1`in`K<x,y>`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]].@return: an element of the current field which is the leading term of

`F`with respect to the current ordering. If`F=0`, then`0`will be returned.

#### Example

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

### See also