Difference between revisions of "ApCoCoA-1:NCo.BInterreduction"

NCo.BInterreduction

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

Syntax

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

Description

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 BLW(G\{g}) for all g in G.

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>]]
-------------------------------
```