# ApCoCoA-1:NCo.Multiply

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

## NCo.Multiply

Multiplication of two polynomials in a free monoid ring.

### Syntax

NCo.Multiply(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 *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 multiplication 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.SetFp(3); NCo.SetX("abc"); NCo.RingEnv(); Coefficient ring : Fp = Z/(3) Alphabet : abc Ordering : LLEX ------------------------------- F1 := [[2,"a"],[1,""]]; F2 := [[2,"b"],[1,"ba"]]; NCo.Multiply(F1,F2); -- over F3 [[2, "aba"], [1, "ab"], [1, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F2,F1); [[2, "baa"], [2, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F1,[]); [ ] ------------------------------- NCo.Multiply([],F1); [ ] ------------------------------- NCo.Multiply([],[]); [ ] ------------------------------- NCo.UnsetFp(); NCo.RingEnv(); Coefficient ring : Q Alphabet : abc Ordering : LLEX ------------------------------- NCo.Multiply(F1,F2); -- over Q [[2, "aba"], [4, "ab"], [1, "ba"], [2, "b"]] ------------------------------- NCo.Multiply(F2,F1); [[2, "baa"], [5, "ba"], [2, "b"]] -------------------------------

### See also