# Difference between revisions of "ApCoCoA-1:NC.LC"

## NC.LC

Leading coefficient of a non-zero polynomial in a non-commutative polynomial 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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

• @param F: a non-zero non-commutative polynomial. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial f=2xyx^2-9yx^2x^3+5 is represented as F:=[[2x,y,x^2], [-9y,x^2,x^3], ]. The zero polynomial 0 is represented as the empty LIST [].

• @return: an INT or a RAT, whhich is the leading coefficient of F with respect to the current word ordering.

#### Example

```USE QQ[x[1..2]];
F:= [[x^2], [2x,x], [3x,x],[4x^2]]; -- x^2+2xx+3xx+4x^2
NC.SetOrdering("LLEX");
NC.LC(F);


-------------------------------
NC.SetOrdering("LRLEX");
NC.LC(F);


-------------------------------
NC.SetOrdering("ELIM");
NC.LC(F);


-------------------------------
NC.SetOrdering("DEGRLEX");
NC.LC(F);


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