# ApCoCoA-1:NCo.Add

This article is about a function from ApCoCoA-1. |

## NCo.Add

Addition of two polynomials in a free monoid ring.

### Syntax

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

@param

*F1, F2:*two polynomials in`K<X>`, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of monomials, which are LISTs of the form [C, W] where W is a word in`<X>`and C is the coefficient of W. For example, the polynomial`f=xy-y+1`is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial`0`is represented as the empty LIST [].@return: a LIST, which represents the polynomial equal to

`F1+F2`.

#### Example

NCo.SetX("abc"); NCo.SetOrdering("ELIM"); NCo.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : ELIE ------------------------------- F1 := [[1,"a"],[1,""]]; F2 := [[1,"b"],[1,"ba"]]; NCo.Add(F1,F2); -- over Q [[1, "ba"], [1, "a"], [1, "b"], [1, ""]] ------------------------------- NCo.SetFp(); -- set default Fp = F2 NCo.RingEnv(); Coefficient ring : Fp = Z/(2) Alphabet : abc Ordering : ELIM ------------------------------- NCo.Add(F1,F2); -- over F2 [[1, "ba"], [1, "a"], [1, "b"], [1, ""]] ------------------------------- NCo.Add(F1,F1); -- over F2 [ ] -------------------------------

### See also