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

## NCo.BNR

The normal remainder of a polynomial with respect to a LIST of polynomials in a free monoid ring over the binary field F_{2}={0,1}.

### Syntax

NCo.BNR(F:LIST, G:LIST):INT

### 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 the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

• @param F: a polynomial 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 [].

• @param G: a LIST of polynomials in the free monoid ring F_{2}<X>.

• @return: a LIST which represents the normal remainder of F with respect to G.

#### Example

NCo.SetX("xyXY");
NCo.SetOrdering("LLEX");
F1:=["xX",""];
F2:=["Xx",""];
F3:=["yY",""];
F4:=["Yy",""];
G:=[F1,F2,F3,F4];
F:=["xyYxxXYY"];
NCo.BNR(F,G);
["xxYY"]
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