# ApCoCoA-1:NCo.LC

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## NCo.LC

The leading coefficient of a non-zero 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 the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

• @param F: a non-zero 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("abc");
F:=[[1,"ab"],[2,"aa"],[3,"bb"],[4,"bab"]];
NCo.SetOrdering("ELIM");
NCo.LC(F);
2
-------------------------------
NCo.SetOrdering("LLEX");
NCo.LC(F);
4
-------------------------------
NCo.LC([]); -- 0 polynomial
0
-------------------------------
```