# ApCoCoA-1:NCo.BAdd

## NCo.BAdd

Addition of two polynomials in a free monoid ring over the binary field F_{2}={0,1}.

### Syntax

NCo.BAdd(F1:LIST, F2: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 the length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.

@param

*F1,F2:*two polynomials in the free monoid ring`F_{2}<X>`, which are left and right operands of addition respectively. 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 which represents the polynomial equal to

`F1+F2`.

#### Example

NCo.SetX(<quotes>xX</quotes>); NCo.SetOrdering(<quotes>LLEX</quotes>); F1:=[<quotes>xX</quotes>,<quotes></quotes>]; F2:=[<quotes>Xx</quotes>,<quotes></quotes>]; NCo.BAdd(F1,F2); [<quotes>xX</quotes>, <quotes>Xx</quotes>] ------------------------------- NCo.BAdd(F1,F1); [ ] ------------------------------- NCo.BAdd([],F1); [<quotes>xX</quotes>, <quotes></quotes>] -------------------------------

### See also