# ApCoCoA-1:NCo.BInterreduction

## NCo.BInterreduction

Interreduce a LIST of polynomials in a free monoid ring over the binary field.

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

### Syntax

NCo.BInterreduction(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 *alphabet* (or set of indeterminates) `X` and *word ordering* via the functions NCo.SetX and NCo.SetOrdering, respectively, before calling this function. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*G:*a LIST of polynomials in the free monoid ring`F_{2}<X>`. Each polynomial is represented as a LIST of words (or terms) in`<X>`. Each word is represented as a STRING. For example,`xy^2x`is represented as "xyyx", and the identity is represented as the empty string "". Thus, the polynomial`f=xy-y+1`is represented as F:=["xy", "y", ""]. 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>); Polynomials:=[[<quotes>ba</quotes>,<quotes>c</quotes>],[<quotes>b</quotes>,<quotes></quotes>], [<quotes>c</quotes>]]; NCo.BInterreduction(Polynomials); [[<quotes>a</quotes>], [<quotes>b</quotes>, <quotes></quotes>], [<quotes>c</quotes>]] -------------------------------

### See also