# 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(<quotes>xyXY</quotes>); NCo.SetOrdering(<quotes>LLEX</quotes>); F1:=[<quotes>xX</quotes>,<quotes></quotes>]; F2:=[<quotes>Xx</quotes>,<quotes></quotes>]; F3:=[<quotes>yY</quotes>,<quotes></quotes>]; F4:=[<quotes>Yy</quotes>,<quotes></quotes>]; G:=[F1,F2,F3,F4]; F:=[<quotes>xyYxxXYY</quotes>]; NCo.BNR(F,G); [<quotes>xxYY</quotes>] -------------------------------

### See also