# ApCoCoA-1:NC.LC

## NC.LC

Leading coefficient of a polynomial over a free monoid ring.

### Syntax

```NC.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 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 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 an empty LIST [].

• @return: a INT or RAT which represents the leading coefficient of F w.r.t. the current ordering. If F=0, the function returns 0.

#### 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

-------------------------------
```