# ApCoCoA-1:NC.Add

## NC.Add

Addition of two polynomials in a non-commutative polynomial ring.

### Syntax

NC.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 non-commutative polynomial ring (via the command Use) and word ordering (via the function NC.SetOrdering) before calling this function. The default word ordering is the length-lexicographic ordering ("LLEX"). For more information, please check the relevant commands and functions.

@param

*F1, F2:*two non-commutative polynomials, which are left and right operands of addition respectively. Each polynomial is represented as a LIST of LISTs, and each element in every inner LIST involves only one indeterminate or none (a constant). For example, the polynomial`f=2x[2]y[1]x[2]^2-9y[2]x[1]^2x[2]^3+5`is represented as F:=[[2x[1],y[1],x[2]^2], [-9y[2],x[1]^2,x[2]^3], [5]]. The zero polynomial`0`is represented as the empty LIST [].@return: a LIST which represents the polynomial equal to

`F1+F2`.

#### Example

USE ZZ/(31)[x[1..2],y[1..2]]; F1:= [[2x[1],y[1],x[2]^2], [13y[2],x[1]^2,x[2]^3], [5]]; F2:= [[2x[1],y[2],x[2]^2], [19y[2],x[1]^2,x[2]^3], [2]]; NC.Add(F1,F2); [[y[2], x[1]^2, x[2]^3], [2x[1], y[1], x[2]^2], [2x[1], y[2], x[2]^2], [7]] -------------------------------

### See also