# Difference between revisions of "ApCoCoA-1:NCo.Interreduction"

## NCo.Interreduction

Interreduce a LIST of polynomials in a free monoid ring.

Note that, given an word ordering Ordering, a set of non-zero polynomials G is called interreduced with respect to Ordering if no element of Supp(g) is contained in the leading word ideal LW(G\{g}) for all g in G.

### Syntax

```NCo.Interreduction(G:LIST):LIST
```

### 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 G: a LIST of polynomials 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 LIST of interreduced polynomials.

#### Example

```NCo.SetX(<quotes>abc</quotes>);
NCo.SetOrdering(<quotes>ELIM</quotes>);
G:=[[[1,<quotes>ba</quotes>]], [[1,<quotes>b</quotes>],[1,<quotes></quotes>]], [[1,<quotes>c</quotes>]]];
NCo.Interreduction(G);

[[[1, <quotes>a</quotes>]], [[1, <quotes>b</quotes>], [1, <quotes></quotes>]], [[1, <quotes>c</quotes>]]]
-------------------------------
```