# ApCoCoA-1:NCo.IsHomog

## NCo.IsHomog

Check whether a polynomial or a list of polynomials is homogeneous in a free monoid ring.

### Syntax

NCo.IsHomog(F:LIST):BOOL

### 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` via the function NCo.SetX before calling the function. For more information, please check the relevant functions.

@param

*F*: a polynomial or a LIST of polynomials in`K<X>`. Each polynomial is represented as a LIST of monomials, which are pairs 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 BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.

#### Example

NCo.SetX(<quotes>xy</quotes>); F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; F := [F1,F2]; NCo.IsHomog(F); False ------------------------------- NCo.IsHomog(F1); True ------------------------------- NCo.IsHomog(F2); False -------------------------------

### See also