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