# 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("xy");
F1 := [[1,"x"], [1,"y"]];
F2 := [[1,"xx"],[1,"xy"],[1,"x"]];
F := [F1,F2];
NCo.IsHomog(F);
False
-------------------------------
NCo.IsHomog(F1);
True
-------------------------------
NCo.IsHomog(F2);
False
-------------------------------
```